NCERT Exemplar for Class 8, Maths Chapter 3

NCERT Exemplar Class 8 Maths Chapter 3: Square-Square Root and Cube-Cube Root. NCERT Exemplar Solutions for Class 8 Maths Chapter 3 Square-Square Root and Cube-Cube Root prepare students for their Class 8 exams thoroughly.

Maths problems and solutions for the Class 8 pdf are provided here which are similar to the questions being asked in the previous year’s board.

NCERT Exemplar Class 8 Maths Chapter 3: Square-Square Root and Cube-Cube Root

Class 8: Maths Chapter 3 solutions. Complete Class 8 Maths Chapter 3 Notes.

Main Concepts and Results

A natural number is called a perfect square if it is the square of some natural number. i.e., if m = n2, then m is a perfect square where m and n are natural numbers.
A natural number is called a perfect cube if it is the cube of some natural number. i.e., if m = n3, then m is a perfect cube where m and n are natural numbers
Number obtained when a number is multiplied by itself is called the square of the number.
Number obtained when a number is multiplied by itself three times are called cube number cube number.
Squares and cubes of even numbers are even and Squares and cubes of odd numbers are odd.
A perfect square can always be expressed as the product of pairs of prime factors.
A perfect cube can always be expressed as the product of triplets of prime factors.
The unit digit of a perfect square can be only 0, 1, 4, 5, 6 or 9.
The square of a number having:
1 or 9 at the units place ends in1.
2 or 8 at the units place ends in 4.
3 or 7 at the units place ends in 9.
4 or 6 at the units place ends in 6.
5 at the units place ends in 5.
There are 2n natural numbers between the squares of numbers n and n+1.
A number ending in odd numbers of zeroes is not a perfect square.
The sum of first n odd natural numbers is given by n2
Three natural numbers a, b, c are said to form a pythagorean triplet if a2 + b2 = c2.
For every natural number m > 1, 2m, m2–1 and m2 + 1 form a pythagorean triplet.
The square root of a number x is the number whose square is x. Positive square root of a number x is denoted by x .
The cube root of a number x is the number whose cube is x. It is denoted by 3 x .
Square root and cube root are the inverse operations of squares and cubes respectively.
If a perfect square is of n digits, then its square root will have n/2 digit if n is even or
digit if n is odd.
Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively.

Key Notes

SQUARE ROOTS

Words A square root of a number n is a number m which, when multiplied by itself, equals n.

Numbers The square roots of 16 are 4 and – 4 because 42 = 16 and (– 4)2 = 16.

Algebra If m2 = n, then m is a square root of n.

Think and Discuss

Which type of number has an exact square root?
Which type of number has an approximate square root?
How can we use perfect squares to estimate a square root, such as √8 ?

⊳ Cube of the number ending in 2 ends in 8 and cube root of the number ending in 8 ends in 2.

⊳ Cube of the number ending in 3 ends in 7 and cube root of the number ending in 7 ends in 3.

Solved Examples

Fill in the Blanks

Connect

Statements are true (T) or false (F)

Connet

Think and Discuss

Is 1 a square number? How can you tell?
Suppose you know the area of a square. How can you find its perimeter?
Suppose you know the perimeter of a square. How can you find its area?

Think and Discuss

Compare your strategies and results with those of another pair of
classmates.
Find two areas greater than 20 square units for which you could use tiles
to make a square
How do you know you could make a square for each of these areas?