{"id":545347,"date":"2021-10-04T09:29:30","date_gmt":"2021-10-04T09:29:30","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=545347"},"modified":"2021-10-27T07:15:31","modified_gmt":"2021-10-27T07:15:31","slug":"rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/","title":{"rendered":"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation"},"content":{"rendered":"\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">Class 9: Maths Chapter 3 solutions. Complete Class 9 Maths Chapter 3 Notes.<\/p>\n\n\n\n<p>RD Sharma Class 9 Solutions Chapter 3<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\">RD Sharma Solutions for Class 9 Maths Chapter 3\u2013Rationalisation<\/h2>\n\n\n\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">RD Sharma 9th Maths Chapter 3, Class 9 Maths Chapter 3 solutions<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 3.1 Solutions<\/h4>\n\n\n\n<p><strong>Question 1: Simplify each of the following:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"113\" height=\"82\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class-9-maths-chapter-3-rationalisation.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545351\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p><strong>(i)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class-9-maths-chapter-3-rationalisation-1.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545352\" width=\"206\" height=\"191\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(ii)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"151\" height=\"296\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class-9-maths-chapter-3-rationalisation-2.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545353\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>Question 2: Simplify the following expressions:<\/strong><\/p>\n\n\n\n<p><strong>(i) (4 + \u221a7) (3 + \u221a2)<\/strong><\/p>\n\n\n\n<p><strong>(ii) (3 + \u221a3)(5- \u221a2 )<\/strong><\/p>\n\n\n\n<p><strong>(iii) (\u221a5 -2)( \u221a3 \u2013 \u221a5)<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>(i)<\/strong>&nbsp;(4 + \u221a7) (3 + \u221a2)<\/p>\n\n\n\n<p>= 12 + 4\u221a2 + 3\u221a7 + \u221a14<\/p>\n\n\n\n<p><strong>(ii)<\/strong>&nbsp;(3 + \u221a3)(5- \u221a2 )<\/p>\n\n\n\n<p>= 15 \u2013 3\u221a2 + 5\u221a3 \u2013 \u221a6<\/p>\n\n\n\n<p><strong>(iii)<\/strong>&nbsp;(\u221a5 -2)( \u221a3 \u2013 \u221a5)<\/p>\n\n\n\n<p>= \u221a15 \u2013 \u221a25 \u2013 2\u221a3 + 2\u221a5<\/p>\n\n\n\n<p>= \u221a15 \u2013 5 \u2013 2\u221a3 + 2\u221a5<\/p>\n\n\n\n<p><strong>Question 3: Simplify the following expressions:<\/strong><\/p>\n\n\n\n<p><strong>(i) (11 + \u221a11) (11 \u2013 \u221a11)<\/strong><\/p>\n\n\n\n<p><strong>(ii) (5 + \u221a7) (5 \u2013\u221a7 )<\/strong><\/p>\n\n\n\n<p><strong>(iii) (\u221a8 \u2013 \u221a2 ) (\u221a8 + \u221a2 )<\/strong><\/p>\n\n\n\n<p><strong>(iv) (3 + \u221a3) (3 \u2013 \u221a3)<\/strong><\/p>\n\n\n\n<p><strong>(v) (\u221a5 \u2013 \u221a2) (\u221a5 + \u221a2)<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>Using Identity: (a \u2013 b)(a+b) = a<sup>2<\/sup>&nbsp;\u2013 b<sup>2<\/sup><\/p>\n\n\n\n<p><strong>(i)<\/strong>&nbsp;(11 + \u221a11) (11 \u2013 \u221a11)<\/p>\n\n\n\n<p>= 11<sup>2<\/sup>&nbsp;\u2013 (\u221a11)<sup>2<\/sup><\/p>\n\n\n\n<p>= 121 \u2013 11<\/p>\n\n\n\n<p>= 110<\/p>\n\n\n\n<p><strong>(ii)<\/strong>&nbsp;(5 + \u221a7) (5 \u2013\u221a7 )<\/p>\n\n\n\n<p>= (5<sup>2<\/sup>&nbsp;\u2013 (\u221a7)<sup>2<\/sup>&nbsp;)<\/p>\n\n\n\n<p>= 25 \u2013 7 = 18<\/p>\n\n\n\n<p><strong>(iii)<\/strong>&nbsp;(\u221a8 \u2013 \u221a2 ) (\u221a8 + \u221a2 )<\/p>\n\n\n\n<p>= (\u221a8)<sup>2<\/sup>&nbsp;\u2013 (\u221a2 )&nbsp;<sup>2<\/sup><\/p>\n\n\n\n<p>= 8 -2<\/p>\n\n\n\n<p>= 6<\/p>\n\n\n\n<p><strong>(iv)<\/strong>&nbsp;(3 + \u221a3) (3 \u2013 \u221a3)<\/p>\n\n\n\n<p>= (3)<sup>2<\/sup>&nbsp;\u2013 (\u221a3)<sup>2<\/sup><\/p>\n\n\n\n<p>= 9 \u2013 3<\/p>\n\n\n\n<p>= 6<\/p>\n\n\n\n<p><strong>(v)<\/strong>&nbsp;(\u221a5 \u2013 \u221a2) (\u221a5 + \u221a2)<\/p>\n\n\n\n<p>=(\u221a5)<sup>2<\/sup>&nbsp;\u2013 (\u221a2)<sup>2<\/sup><\/p>\n\n\n\n<p>= 5 \u2013 2<\/p>\n\n\n\n<p>= 3<\/p>\n\n\n\n<p><strong>Question 4: Simplify the following expressions:<\/strong><\/p>\n\n\n\n<p><strong>(i) (\u221a3 + \u221a7)<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(ii) (\u221a5 \u2013 \u221a3)<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(iii) (2\u221a5 + 3\u221a2 )<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>Using identities: (a \u2013 b)<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ b<sup>2<\/sup>&nbsp;\u2013 2ab and (a + b)<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ b<sup>2<\/sup>&nbsp;+ 2ab<\/p>\n\n\n\n<p><strong>(i)<\/strong>&nbsp;(\u221a3 + \u221a7)<sup>2<\/sup><\/p>\n\n\n\n<p>= (\u221a3)<sup>2<\/sup>&nbsp;+ (\u221a7)<sup>2<\/sup>&nbsp;+ 2(\u221a3)( \u221a7)<\/p>\n\n\n\n<p>= 3 + 7 + 2\u221a21<\/p>\n\n\n\n<p>= 10 + 2\u221a21<\/p>\n\n\n\n<p><strong>(ii)<\/strong>&nbsp;(\u221a5 \u2013 \u221a3)<sup>2<\/sup><\/p>\n\n\n\n<p>= (\u221a5)<sup>2<\/sup>&nbsp;+ (\u221a3)<sup>2&nbsp;<\/sup>\u2013 2(\u221a5)( \u221a3)<\/p>\n\n\n\n<p>= 5 + 3 \u2013 2\u221a15<\/p>\n\n\n\n<p>= 8 \u2013 2\u221a15<\/p>\n\n\n\n<p><strong>(iii)<\/strong>&nbsp;(2\u221a5 + 3\u221a2 )<sup>2<\/sup><\/p>\n\n\n\n<p>= (2\u221a5)<sup>2<\/sup>&nbsp;+ (3\u221a2 )<sup>2&nbsp;<\/sup>+ 2(2\u221a5 )( 3\u221a2)<\/p>\n\n\n\n<p>= 20 + 18 + 12\u221a10<\/p>\n\n\n\n<p>= 38 + 12\u221a10<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 3.2<\/h4>\n\n\n\n<p><strong>Question 1: Rationalise the denominators of each of the following (i \u2013 vii):<\/strong><\/p>\n\n\n\n<p><strong>(i) 3\/ \u221a5 (ii) 3\/(2 \u221a5) (iii) 1\/ \u221a12 (iv) \u221a2\/ \u221a5<\/strong><\/p>\n\n\n\n<p><strong>(v) (\u221a3 + 1)\/ \u221a2 (vi) (\u221a2 + \u221a5)\/ \u221a3 (vii) 3 \u221a2\/ \u221a5<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p><strong>(i)&nbsp;<\/strong>Multiply both numerator and denominator to with same number to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"94\" height=\"97\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545354\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p>= 3\u221a5\/5<\/p>\n\n\n\n<p><strong>(ii)<\/strong>&nbsp;Multiply both numerator and denominator to with same number to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"221\" height=\"127\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-1.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545355\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(iii)<\/strong>&nbsp;Multiply both numerator and denominator to with same number to rationalise the denominator.<\/p>\n\n\n\n\n\n<p><strong>(iv)<\/strong>&nbsp;Multiply both numerator and denominator to with same number to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"267\" height=\"66\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-3.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545356\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(v)<\/strong>&nbsp;Multiply both numerator and denominator to with same number to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"277\" height=\"72\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-4.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545357\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(vi)<\/strong>&nbsp;Multiply both numerator and denominator to with same number to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"141\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-5.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545358\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(vii)<\/strong>&nbsp;Multiply both numerator and denominator to with same number to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"231\" height=\"118\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-6.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545359\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>Question 2: Find the value to three places of decimals of each of the following. It is given that<\/strong><\/p>\n\n\n\n<p><strong>\u221a2 = 1.414, \u221a3 = 1.732, \u221a5 = 2.236 and \u221a10 = 3.162<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"292\" height=\"207\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-7.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545360\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"272\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-8.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545361\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-8.png 344w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-8-300x237.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/figure>\n\n\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"335\" height=\"248\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-10.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545362\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-10.png 335w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-10-300x222.png 300w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/figure>\n\n\n\n<p><strong>Question 3: Express each one of the following with rational denominator:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"206\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-11.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545363\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-11.png 407w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-11-300x152.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-11-400x202.png 400w\" sizes=\"auto, (max-width: 407px) 100vw, 407px\" \/><\/figure>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>Using identity: (a + b) (a \u2013 b) = a<sup>2<\/sup>&nbsp;\u2013 b<sup>2<\/sup><\/p>\n\n\n\n<p><strong>(i)<\/strong>&nbsp;Multiply and divide given number by 3\u2212\u221a2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"155\" height=\"239\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-12.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545364\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(ii)<\/strong>&nbsp;Multiply and divide given number by \u221a6 + \u221a5<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"190\" height=\"235\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-13.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545365\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(iii)<\/strong>&nbsp;Multiply and divide given number by \u221a41 + 5<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"172\" height=\"333\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-14.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545366\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-14.png 172w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-14-155x300.png 155w\" sizes=\"auto, (max-width: 172px) 100vw, 172px\" \/><\/figure>\n\n\n\n<p><strong>(iv)<\/strong>&nbsp;Multiply and divide given number by 5\u221a3 + 3\u221a5<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"237\" height=\"283\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-15.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545367\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(v)<\/strong>&nbsp;Multiply and divide given number by 2\u221a5 + \u221a3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"199\" height=\"240\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-16.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545368\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(vi)<\/strong>&nbsp;Multiply and divide given number by 2\u221a2 + \u221a3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"198\" height=\"259\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-17.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545369\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(vii)<\/strong>&nbsp;Multiply and divide given number by 6 \u2013 4\u221a2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"405\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-18.png\" alt=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" class=\"wp-image-545370\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-18.png 179w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-18-133x300.png 133w\" sizes=\"auto, (max-width: 179px) 100vw, 179px\" \/><\/figure>\n\n\n\n<p><strong>(viii)<\/strong>&nbsp;Multiply and divide given number by 2\u221a5 + 3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"212\" height=\"254\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-19.png\" alt=\"\" class=\"wp-image-545371\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(ix)<\/strong>&nbsp;Multiply and divide given number by \u221a(a<sup>2<\/sup>+b<sup>2<\/sup>) \u2013 a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"265\" height=\"327\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-20.png\" alt=\"\" class=\"wp-image-545372\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-20.png 265w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-20-243x300.png 243w\" sizes=\"auto, (max-width: 265px) 100vw, 265px\" \/><\/figure>\n\n\n\n<p><strong>Question 4: Rationales the denominator and simplify:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"429\" height=\"127\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-21.png\" alt=\"\" class=\"wp-image-545373\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-21.png 429w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-21-300x89.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-21-400x118.png 400w\" sizes=\"auto, (max-width: 429px) 100vw, 429px\" \/><\/figure>\n\n\n\n<p><strong>Solution<\/strong>:[Use identities: (a + b) (a \u2013 b) = a<sup>2<\/sup>&nbsp;\u2013 b<sup>2<\/sup>&nbsp;; (a + b)<sup>2<\/sup>&nbsp;= (a<sup>2<\/sup>&nbsp;+ 2ab + b<sup>2<\/sup>&nbsp;and (a \u2013 b)<sup>2<\/sup>&nbsp;= (a<sup>2<\/sup>&nbsp;\u2013 2ab + b<sup>2<\/sup>&nbsp;]<\/p>\n\n\n\n<p><strong>(i)<\/strong>&nbsp;Multiply both numerator and denominator by \u221a3\u2013\u221a2 to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"178\" height=\"302\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-22.png\" alt=\"\" class=\"wp-image-545374\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-22.png 178w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-22-177x300.png 177w\" sizes=\"auto, (max-width: 178px) 100vw, 178px\" \/><\/figure>\n\n\n\n<p><strong>(ii)<\/strong>&nbsp;Multiply both numerator and denominator by 7\u20134\u221a3 to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"274\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-23.png\" alt=\"\" class=\"wp-image-545375\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(iii)<\/strong>&nbsp;Multiply both numerator and denominator by 3+2\u221a2 to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"241\" height=\"255\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-24.png\" alt=\"\" class=\"wp-image-545376\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>(iv)<\/strong>&nbsp;Multiply both numerator and denominator by 3\u221a5+2\u221a6 to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"218\" height=\"356\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-25.png\" alt=\"\" class=\"wp-image-545377\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-25.png 218w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-25-184x300.png 184w\" sizes=\"auto, (max-width: 218px) 100vw, 218px\" \/><\/figure>\n\n\n\n<p><strong>(v)<\/strong>&nbsp;Multiply both numerator and denominator by \u221a48\u2013\u221a18 to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"359\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-26.png\" alt=\"\" class=\"wp-image-545378\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-26.png 228w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-26-191x300.png 191w\" sizes=\"auto, (max-width: 228px) 100vw, 228px\" \/><\/figure>\n\n\n\n<p><strong>(vi)<\/strong>&nbsp;Multiply both numerator and denominator by 2\u221a2 \u2013 3\u221a3 to rationalise the denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"222\" height=\"300\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-ex-3-2-question-27.png\" alt=\"\" class=\"wp-image-545379\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise VSAQs<\/h4>\n\n\n\n<p><strong>Question 1: Write the value of (2 + \u221a3) (2 \u2013 \u221a3).<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>(2 + \u221a3) (2 \u2013 \u221a3)<\/p>\n\n\n\n<p>= (2)<sup>2<\/sup>&nbsp;\u2013 (\u221a3)<sup>2<\/sup>[Using identity : (a + b)(a \u2013 b) = a<sup>2<\/sup>&nbsp;\u2013 b<sup>2<\/sup>]<\/p>\n\n\n\n<p>= 4 \u2013 3<\/p>\n\n\n\n<p>= 1<\/p>\n\n\n\n<p><strong>Question 2: Write the reciprocal of 5 + \u221a2.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"338\" height=\"321\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu.png\" alt=\"\" class=\"wp-image-545380\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu.png 338w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-300x285.png 300w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><\/figure>\n\n\n\n<p><strong>Question 3: Write the rationalisation factor of 7 \u2013 3\u221a5.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>Rationalisation factor of 7 \u2013 3\u221a5 is 7 + 3\u221a5<\/p>\n\n\n\n<p><strong>Question 4: If<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"61\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-1.png\" alt=\"\" class=\"wp-image-545381\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>Find the values of x and y.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:[Using identities : (a + b)(a \u2013 b) = a<sup>2<\/sup>&nbsp;\u2013 b<sup>2&nbsp;<\/sup>and (a \u2013 b)<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ b<sup>2<\/sup>&nbsp;\u2013 2ab]<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"357\" height=\"278\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-2.png\" alt=\"\" class=\"wp-image-545382\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-2.png 357w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-2-300x234.png 300w\" sizes=\"auto, (max-width: 357px) 100vw, 357px\" \/><\/figure>\n\n\n\n<p><strong>Question 5: If x = \u221a2 \u2013 1, then write the value of 1\/x.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>x = \u221a2 \u2013 1<\/p>\n\n\n\n<p>or 1\/x = 1\/(\u221a2 \u2013 1)<\/p>\n\n\n\n<p>Rationalising denominator, we have<\/p>\n\n\n\n<p>= 1\/(\u221a2 \u2013 1) x (\u221a2 + 1)\/(\u221a2 + 1)<\/p>\n\n\n\n<p>= (\u221a2 + 1)\/(2-1)<\/p>\n\n\n\n<p>= \u221a2 + 1<\/p>\n\n\n\n<p><strong>Question 6: Simplify<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"78\" height=\"35\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-3.png\" alt=\"\" class=\"wp-image-545383\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"172\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-4.png\" alt=\"\" class=\"wp-image-545384\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p>[ Because: (a + b)<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ b<sup>2<\/sup>&nbsp;+ 2ab ]<\/p>\n\n\n\n<p><strong>Question 7: Simplify<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"88\" height=\"32\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-5.png\" alt=\"\" class=\"wp-image-545385\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"216\" height=\"173\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-6.png\" alt=\"\" class=\"wp-image-545386\" title=\"RD Sharma Solutions Class 9 Rationalisation\"\/><\/figure>\n\n\n\n<p>[ Because: (a \u2013 b)<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ b<sup>2<\/sup>&nbsp;\u2013 2ab ]<\/p>\n\n\n\n<p><strong>Question 8:&nbsp;<\/strong>If a = \u221a2 +1, then find the value of a \u2013 1\/a.<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>Given: a = \u221a2 + 1<\/p>\n\n\n\n<p>1\/a = 1\/(\u221a2 + 1)<\/p>\n\n\n\n<p>= 1\/(\u221a2 + 1) x (\u221a2 \u2013 1)\/(\u221a2 \u2013 1)<\/p>\n\n\n\n<p>= (\u221a2 \u2013 1)\/ ((\u221a2)<sup>2<\/sup>&nbsp;\u2013 (1)<sup>2<\/sup>)<\/p>\n\n\n\n<p>= (\u221a2 \u2013 1)\/1<\/p>\n\n\n\n<p>= \u221a2 \u2013 1<\/p>\n\n\n\n<p>Now,<\/p>\n\n\n\n<p>a \u2013 1\/a = (\u221a2 + 1) \u2013 (\u221a2 \u2013 1)<\/p>\n\n\n\n<p>= 2<\/p>\n\n\n\n<p><strong>Question 9: If x = 2 + \u221a3, find the value of x + 1\/x.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given: x = 2 + \u221a3<\/p>\n\n\n\n<p>1\/x = 1\/(2 + \u221a3)<\/p>\n\n\n\n<p>= 1\/(2 + \u221a3) x (2 \u2013 \u221a3)\/(2 \u2013 \u221a3)<\/p>\n\n\n\n<p>= (2 \u2013 \u221a3)\/ ((2)<sup>2<\/sup>&nbsp;\u2013 (\u221a3)<sup>2<\/sup>)<\/p>\n\n\n\n<p>= (2 \u2013 \u221a3)\/(4-3)<\/p>\n\n\n\n<p>= (2 \u2013 \u221a3)<\/p>\n\n\n\n<p>Now,<\/p>\n\n\n\n<p>x + 1\/x = (2 + \u221a3) + (2 \u2013 \u221a3)<\/p>\n\n\n\n<p>= 4<\/p>\n\n\n\n<p><strong>Question 10: Write the rationalisation factor of \u221a5 \u2013 2.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Rationalisation factor of \u221a5 \u2013 2 is \u221a5 + 2<\/p>\n\n\n\n<p><strong>Question 11: If x = 3 + 2\u221a2, then find the value of \u221ax \u2013 1\/\u221ax.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"310\" height=\"377\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-7.png\" alt=\"\" class=\"wp-image-545387\" title=\"RD Sharma Solutions Class 9 Rationalisation\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-7.png 310w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/rd-sharma-class-9-maths-chapter-3-short-answers-qu-7-247x300.png 247w\" sizes=\"auto, (max-width: 310px) 100vw, 310px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-9-maths-chapter-3-download-pdf\">RD Sharma Solutions for Class 9 Maths Chapter 3:&nbsp;<strong>Download PDF<\/strong><\/h2>\n\n\n\n<p>RD Sharma Solutions for Class 9 Maths Chapter 3\u2013Rationalisation<\/p>\n\n\n\n<p><a href=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/RD-Sharma-Solutions-for-Class-9-Maths-Chapter-3\u2013Rationalisation.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download PDF<\/strong>: RD Sharma Solutions for Class 9 Maths Chapter 3\u2013Rationalisation PDF<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Chapterwise RD Sharma Solutions for Class 9&nbsp;Maths :<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-1-number-system\/\">Chapter 1\u2013Number System<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-2-exponents-of-real-numbers\/\">Chapter 2\u2013Exponents of Real Numbers<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\">Chapter 3\u2013Rationalisation<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-4-algebraic-identities\/\">Chapter 4\u2013Algebraic Identities<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-5-factorization-of-algebraic-expressions\/\">Chapter 5\u2013Factorization of Algebraic Expressions<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-6-factorization-of-polynomials\/\">Chapter 6\u2013Factorization Of Polynomials<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-7-introduction-to-euclids-geometry\/\">Chapter 7\u2013Introduction to Euclid\u2019s Geometry<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-8-lines-and-angles\/\">Chapter 8\u2013Lines and Angles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-9-triangle-and-its-angles\/\">Chapter 9\u2013Triangle and its Angles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-10-congruent-triangles\/\">Chapter 10\u2013Congruent Triangles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-11-co-ordinate-geometry\/\">Chapter 11\u2013Coordinate Geometry<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-12-herons-formula\/\">Chapter 12\u2013Heron\u2019s Formula<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-13-linear-equations-in-two-variables\/\">Chapter 13\u2013Linear Equations in Two Variables<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-14-quadrilaterals\/\">Chapter 14\u2013Quadrilaterals<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-15-area-of-parallelograms-and-triangles\/\">Chapter 15\u2013Area of Parallelograms and Triangles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-16-circles\/\">Chapter 16\u2013Circles<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-17-construction\/\">Chapter 17\u2013Construction<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-18-surface-area-and-volume-of-cuboid-and-cube\/\">Chapter 18\u2013Surface Area and Volume of Cuboid and Cube<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-19-surface-area-and-volume-of-a-right-circular-cylinder\/\">Chapter 19\u2013Surface Area and Volume of A Right Circular Cylinder<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-20-surface-area-and-volume-of-a-right-circular-cone\/\">Chapter 20\u2013Surface Area and Volume of A Right Circular Cone<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-21-surface-area-and-volume-of-sphere\/\">Chapter 21\u2013Surface Area And Volume Of Sphere<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-22-tabular-representation-of-statistical-data\/\">Chapter 22\u2013Tabular Representation of Statistical Data<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-23-graphical-representation-of-statistical-data\/\">Chapter 23\u2013Graphical Representation of Statistical Data<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-24-measure-of-central-tendency\/\">Chapter 24\u2013Measure of Central Tendency<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-25-probability\/\">Chapter 25\u2013Probability<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">About RD Sharma<\/h2>\n\n\n\n<p>RD Sharma i<em>sn&#8217;t the kind of author you&#8217;d bump into at lit fests. But his bestselling books have helped many&nbsp;<\/em>CBSE<em>&nbsp;students lose their dread of&nbsp;<\/em>maths<em>. Sunday Times profiles the tutor turned internet star<\/em><br>He dreams of algorithms that would give most people nightmares. And, spends every waking hour thinking of ways to explain concepts like &#8216;series solution of linear differential equations&#8217;. Meet Dr&nbsp;Ravi Dutt Sharma&nbsp;\u2014&nbsp;mathematics&nbsp;teacher and author of 25 reference books \u2014 whose name evokes as much awe as the subject he teaches. And though students have used his thick tomes for the last 31 years to ace the dreaded maths exam, it&#8217;s only recently that a spoof video turned the tutor into a YouTube star.<\/p>\n\n\n\n<p>R D Sharma had a good laugh but said he shared little with his on-screen persona except for the love for maths. &#8220;I like to spend all my time thinking and writing about maths problems. I find it relaxing,&#8221; he says. When he is not writing books explaining mathematical concepts for classes 6 to 12 and engineering students, Sharma is busy dispensing his duty as vice-principal and head of department of science and humanities at Delhi government&#8217;s Guru Nanak Dev Institute of Technology.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Read More<\/h2>\n\n\n\n<ul class=\"wp-block-yoast-seo-related-links\"><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-1-number-system\/\">RD Sharma Solutions for Class 9 Maths Chapter 1\u2013Number System<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ncert-solutions-for-class-10th-mathematics-chapter-1-real-numbers\/\">NCERT Solutions for Class 10th Mathematics: Chapter 1 Real Numbers<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ncert-solutions-for-5th-class-maths-chapter-13-ways-to-multiply-and-divide\/\">NCERT Solutions for 5th Class Maths Chapter 13- Ways To Multiply And Divide<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-10-maths-chapter-12-some-applications-of-trigonometry\/\">RD Sharma Solutions for Class 10 Maths Chapter 12\u2013Some Applications of Trigonometry<\/a><\/li><li><a href=\"https:\/\/www.indcareer.com\/schools\/ncert-solutions-for-8th-class-maths-chapter-2-linear-equations-in-one-variable-part-ii\/\">NCERT Solutions for 8th Class Maths: Chapter 2-Linear Equations in One Variable Part-II<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Class 9: Maths Chapter 3 solutions. Complete Class 9 Maths Chapter 3 Notes. RD Sharma Class 9 Solutions Chapter 3 RD Sharma Solutions for Class 9 Maths Chapter 3\u2013Rationalisation RD Sharma 9th Maths Chapter 3, Class 9 Maths Chapter 3 solutions Exercise 3.1 Solutions Question 1: Simplify each of the following: Solution: (i) (ii) Question [&hellip;]<\/p>\n","protected":false},"author":302,"featured_media":545350,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[1411,921],"tags":[1962],"boards":[],"class_list":["post-545347","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book-solutions","category-class-9","tag-rd-sharma-solutions","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.1.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>RD Sharma Solutions for Class 9, maths Chapter 3 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation | Browse all Class 9 Maths Chapters RD Sharma books - IndCareer Schools\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\" \/>\n<meta property=\"og:description\" content=\"Class 9: Maths Chapter 3 solutions. Complete Class 9 Maths Chapter 3 Notes. RD Sharma Class 9 Solutions Chapter 3 RD Sharma Solutions for Class 9 Maths\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-04T09:29:30+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-27T07:15:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/i0.wp.com\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png?fit=1200%2C675&ssl=1\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"675\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"15 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\",\"datePublished\":\"2021-10-04T09:29:30+00:00\",\"dateModified\":\"2021-10-27T07:15:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\"},\"wordCount\":1088,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png\",\"keywords\":[\"RD Sharma Solutions\"],\"articleSection\":[\"Book Solutions\",\"class 9\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\",\"name\":\"RD Sharma Solutions for Class 9, maths Chapter 3 - IndCareer Schools\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png\",\"datePublished\":\"2021-10-04T09:29:30+00:00\",\"dateModified\":\"2021-10-27T07:15:31+00:00\",\"description\":\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation | Browse all Class 9 Maths Chapters RD Sharma books - IndCareer Schools\",\"breadcrumb\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage\",\"url\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png\",\"contentUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png\",\"width\":1200,\"height\":675,\"caption\":\"RD Sharma Solutions for Class 9 Maths Chapter 3\u2013Rationalisation\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.indcareer.com\/schools\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"class 9\",\"item\":\"https:\/\/www.indcareer.com\/schools\/class-9\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#website\",\"url\":\"https:\/\/www.indcareer.com\/schools\/\",\"name\":\"IndCareer Schools\",\"description\":\"School Admissions &amp; Notices\",\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.indcareer.com\/schools\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\",\"name\":\"IndCareer\",\"url\":\"https:\/\/www.indcareer.com\/schools\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/06\/indcareer-logo2.png\",\"contentUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/06\/indcareer-logo2.png\",\"width\":512,\"height\":250,\"caption\":\"IndCareer\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/indcareer\",\"https:\/\/x.com\/indcareer\",\"https:\/\/www.youtube.com\/channel\/UC1liU3RZoBRuu8YcAuZMsOQ\"],\"email\":\"info@ebharat.in\",\"legalName\":\"IndCareer\",\"numberOfEmployees\":{\"@type\":\"QuantitativeValue\",\"minValue\":\"1\",\"maxValue\":\"10\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\",\"name\":\"Pooja\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/350f7cfdfb6a23bcab67b56b5e77549db2a13b5d23e63175ac5bd07b5d44b720?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/350f7cfdfb6a23bcab67b56b5e77549db2a13b5d23e63175ac5bd07b5d44b720?s=96&d=mm&r=g\",\"caption\":\"Pooja\"}}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"RD Sharma Solutions for Class 9, maths Chapter 3 - IndCareer Schools","description":"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation | Browse all Class 9 Maths Chapters RD Sharma books - IndCareer Schools","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/","og_locale":"en_US","og_type":"article","og_title":"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation","og_description":"Class 9: Maths Chapter 3 solutions. Complete Class 9 Maths Chapter 3 Notes. RD Sharma Class 9 Solutions Chapter 3 RD Sharma Solutions for Class 9 Maths","og_url":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/","og_site_name":"IndCareer Schools","article_publisher":"https:\/\/www.facebook.com\/indcareer","article_published_time":"2021-10-04T09:29:30+00:00","article_modified_time":"2021-10-27T07:15:31+00:00","og_image":[{"width":1200,"height":675,"url":"https:\/\/i0.wp.com\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png?fit=1200%2C675&ssl=1","type":"image\/png"}],"author":"Pooja","twitter_card":"summary_large_image","twitter_creator":"@indcareer","twitter_site":"@indcareer","twitter_misc":{"Written by":"Pooja","Est. reading time":"15 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#article","isPartOf":{"@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/"},"author":{"name":"Pooja","@id":"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e"},"headline":"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation","datePublished":"2021-10-04T09:29:30+00:00","dateModified":"2021-10-27T07:15:31+00:00","mainEntityOfPage":{"@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/"},"wordCount":1088,"publisher":{"@id":"https:\/\/www.indcareer.com\/schools\/#organization"},"image":{"@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage"},"thumbnailUrl":"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png","keywords":["RD Sharma Solutions"],"articleSection":["Book Solutions","class 9"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/","url":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/","name":"RD Sharma Solutions for Class 9, maths Chapter 3 - IndCareer Schools","isPartOf":{"@id":"https:\/\/www.indcareer.com\/schools\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage"},"image":{"@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage"},"thumbnailUrl":"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png","datePublished":"2021-10-04T09:29:30+00:00","dateModified":"2021-10-27T07:15:31+00:00","description":"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation | Browse all Class 9 Maths Chapters RD Sharma books - IndCareer Schools","breadcrumb":{"@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#primaryimage","url":"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png","contentUrl":"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/10\/class9m3.png","width":1200,"height":675,"caption":"RD Sharma Solutions for Class 9 Maths Chapter 3\u2013Rationalisation"},{"@type":"BreadcrumbList","@id":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-9-maths-chapter-3-rationalisation\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.indcareer.com\/schools\/"},{"@type":"ListItem","position":2,"name":"class 9","item":"https:\/\/www.indcareer.com\/schools\/class-9\/"},{"@type":"ListItem","position":3,"name":"RD Sharma Solutions for Class 9 Maths Chapter 3: Rationalisation"}]},{"@type":"WebSite","@id":"https:\/\/www.indcareer.com\/schools\/#website","url":"https:\/\/www.indcareer.com\/schools\/","name":"IndCareer Schools","description":"School Admissions &amp; Notices","publisher":{"@id":"https:\/\/www.indcareer.com\/schools\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.indcareer.com\/schools\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/www.indcareer.com\/schools\/#organization","name":"IndCareer","url":"https:\/\/www.indcareer.com\/schools\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.indcareer.com\/schools\/#\/schema\/logo\/image\/","url":"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/06\/indcareer-logo2.png","contentUrl":"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/06\/indcareer-logo2.png","width":512,"height":250,"caption":"IndCareer"},"image":{"@id":"https:\/\/www.indcareer.com\/schools\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/indcareer","https:\/\/x.com\/indcareer","https:\/\/www.youtube.com\/channel\/UC1liU3RZoBRuu8YcAuZMsOQ"],"email":"info@ebharat.in","legalName":"IndCareer","numberOfEmployees":{"@type":"QuantitativeValue","minValue":"1","maxValue":"10"}},{"@type":"Person","@id":"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e","name":"Pooja","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/350f7cfdfb6a23bcab67b56b5e77549db2a13b5d23e63175ac5bd07b5d44b720?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/350f7cfdfb6a23bcab67b56b5e77549db2a13b5d23e63175ac5bd07b5d44b720?s=96&d=mm&r=g","caption":"Pooja"}}]}},"_links":{"self":[{"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/posts\/545347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/users\/302"}],"replies":[{"embeddable":true,"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/comments?post=545347"}],"version-history":[{"count":0,"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/posts\/545347\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/media\/545350"}],"wp:attachment":[{"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/media?parent=545347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/categories?post=545347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/tags?post=545347"},{"taxonomy":"boards","embeddable":true,"href":"https:\/\/www.indcareer.com\/schools\/wp-json\/wp\/v2\/boards?post=545347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}