# Squares And Square Roots Chapter 6 Class 8 Maths NCERT PDF

NCERT Solutions for Class 8 Maths Chapter 6′ PDF Quick download link is given at the bottom of this article. You can see the PDF demo, size of the PDF, page numbers, and direct download Free PDF of ‘Ncert Class 8 Maths Chapter 5 Exercise Solution’ using the download button.

### Chapter 6:Squares And Square Roots

#### 6.1 Introduction

You know that the area of a square = side × side (where ‘side’ means ‘the length of a side).

Study the following table.
Side of a square (in cm) Area of the square (in cm2)
1 1 × 1 = 1 = 12
2 2 × 2 = 4 = 22
3 3 × 3 = 9 = 32
5 5 × 5 = 25 = 52
8 8 × 8 = 64 = 82
a a × a = a2
What is special about the numbers 4, 9, 25, 64, and other such numbers?
Since 4 can be expressed as 2 × 2 = 22
, 9 can be expressed as 3 × 3 = 32, all such

numbers can be expressed as the product of the number with itself. Such numbers like 1, 4, 9, 16, 25, … are known as square numbers.

In general, if a natural number m can be expressed as n2, where n is also a natural number, then m is a square number. Is 32 a square number?

We know that 52
= 25 and 62
= 36.

If 32 is a square number, it must be the square of a natural number between 5 and 6. But there is no natural number between 5 and 6. Therefore 32 is not a square number. Consider the following numbers and their squares

### NCERT Solutions Class 8 Maths Chapter 6 Squares And Square Roots

1. What will be the unit digit of the squares of the following numbers?

i. 81

ii. 272

iii. 799

iv. 3853

v. 1234

vi. 26387

vii. 52698

viii. 99880

ix. 12796

x. 55555

Solution:

The unit digit of the square of a number having ‘a’ at its unit place ends with a×a.

i. The unit digit of the square of a number having digit 1 as the unit’s place is 1.

∴ Unit digit of the square of number 81 is equal to 1.

ii. The unit digit of the square of a number having digit 2 as the unit’s place is 4.

∴ Unit digit of the square of the number 272 is equal to 4.

iii. The unit digit of the square of a number having digit 9 as the unit’s place is 1.

∴ Unit digit of the square of number 799 is equal to 1.

iv. The unit digit of the square of a number having digit 3 as the unit’s place is 9.

∴ Unit digit of the square of number 3853 is equal to 9.

v. The unit digit of the square of a number having digit 4 as unit’s place is 6.

∴ Unit digit of the square of number 1234 is equal to 6.

vi. The unit digit of the square of a number having digit 7 as unit’s place is 9.

∴ Unit digit of the square of number 26387 is equal to 9.

vii. The unit digit of the square of a number having digit 8 as unit’s place is 4.

∴ Unit digit of the square of number 52698 is equal to 4.

viii. The unit digit of the square of a number having digit 0 as unit’s place is 01.

∴ Unit digit of the square of the number 99880 is equal to 0.

ix. The unit digit of the square of a number having digit 6 as unit’s place is 6.

∴ Unit digit of the square of number 12796 is equal to 6.

x. The unit digit of the square of a number having digit 5 as unit’s place is 5.

∴ Unit digit of the square of number 55555 is equal to 5.

2. The following numbers are obviously not perfect squares. Give reason.

i. 1057

ii. 23453

iii. 7928

iv. 222222

v. 64000

vi. 89722

vii. 222000

viii. 505050

Solution:

We know that natural numbers ending in the digits 0, 2, 3, 7, and 8 are not perfect squares.

i. 1057 ⟹ Ends with 7

ii. 23453 ⟹ Ends with 3

iii. 7928 ⟹ Ends with 8

iv. 222222 ⟹ Ends with 2

v. 64000 ⟹ Ends with 0

vi. 89722 ⟹ Ends with 2

vii. 222000 ⟹ Ends with 0

viii. 505050 ⟹ Ends with 0