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.

### 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?

### Multiple Choice Questions

Fill in the Blanks Type Questions

True False Type Questions