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## NCERT Class 8 Maths Textbook Chapter 6 With Answer Book PDF Free Download

### 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

Author | NCERT |

Language | English |

No. of Pages | 20 |

PDF Size | 278 KB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### 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

NCERT Class 8 Maths Textbook Chapter 6 With Answer Book PDF Free Download