NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.1.

- Squares and Square Roots Class 8 Ex 6.2
- Squares and Square Roots Class 8 Ex 6.3
- Squares and Square Roots Class 8 Ex 6.4

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 6 |

Chapter Name |
Squares and Square Roots |

Exercise |
Ex 6.1 |

Number of Questions Solved |
9 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.1

**Question 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.**

**(i) 81**

∵ \(1\times 1\)

∴ The unit digit of the square of the number 81 will be 1.

**(ii) 272**

∵ \(2\times 2\)

∴ The unit digit of the square of the number 272 will be 4.

**(iii)** **799**

∵ \(9\times 9\)

∴ The unit digit of the square of the number 799 will be 1.

**(iv)** **3853**

∵ \(3\times 3\)

∴ The unit digit of the square of the number 3853 will be 9

**(v)** **1234**

∵ \(4\times 4\)

∴ The unit digit of the square of the number 1234 will be 6.

**(vi)** **26387**

∵ \(7\times 7\)

∴ The unit digit of the square of the number 26387 will be 9.

**(vii)** **52698**

∵ \(8\times 8\)

∴ The unit digit of the square of the number 52698 will be 4.

**(viii)** **99880**

∵ \(0\times 0\)

∴ The unit digit of the square of the number 99880 will be 0.

**(ix)** **12796**

∵ \(6\times 6\)

∴ The unit digit of the square of the number 12796 will be 6.

**(x)** **55555**

∵ \(5\times 5\)

∴ The unit digit of the square of the number 55555 will be 5.

**Question 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.**

**(i)** **1057**

The number 1057 is not a perfect square because it ends with 7 at unit’s place whereas the square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.

**(ii)** **23453**

The number 23453 is not a perfect square because it ends with 3 at unit’s place whereas the square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.

**(iii)** **7928**

The number 7928 is not a perfect square because it ends with 8 at unit’s place whereas the square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.

**(iv)** **222222**

The number 222222 is not a perfect square because it ends with 2 at unit’s place whereas the Square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.

**(v)** **64000**

The number 64000 is not a square number because it has 3 (an odd number of) zeros at the end whereas the number of zeros at the end of a square number ending with zeros is always even.

**(vi)** **89722**

The number 89722 is not a square number because it ends in 2 at unit’s place whereas the square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.

**(vii)** **222000**

The number 222000 is not a square number because it has 3 (an odd number of) zeros at the end whereas the number of zeros at the end of a square number ending with zeros is always even.

**(viii)** **505050**

The number 505050 is not a square number because it has 1 (an odd number of) zeros at the end whereas the number of zeros at the end of a square number ending with zeros is always even.

**Question 3.**

**The squares of which of the following would be odd numbers ?**

**(i)** 431

**(ii)** 2826

**(iii)** 7779

**(v)** 82004.

**Solution.**

**(i)** **431**

∵ 431 is an odd number

∴ Its square will also be an odd number.

**(ii) 2826**

∵ 2826 is an even number

∴ Its square will not be an odd number.

**(iii) 7779**

∵ 7779 is an odd number

∴ Its square will be an odd number.

**(iv) 82004**

∵ 82004 is an even number

∴ Its square will not be an odd number.

**Question 4.**

Observe the following pattern and find the missing digits:

**Solution.**

**Question 5.**

Observe the following pattern and supply the missing numbers:

**Solution.**

**Question 6.**

Using the given pattern, find the missing numbers:

**Solution.**

**Question 7.**

**Without adding, find the sum:**

**(i)** 1 + 3 + 5+7 + 9

**(ii)** 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +17 + 19

**(iii)** 1+3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 +23.

**Solution.**

**(i)**

l + 3 + 5 + 7 + 9 = sum of first five odd natural numbers = \({ 5 }^{ 2 }\) = 25

**(ii)**

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = sum of first ten odd natural numbers = \({ 10 }^{ 2 }\) = 100

**(iii)**

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = sum of first twelve odd natural numbers = \({ 12 }^{ 2 }\)= 144.

**Question 8.**

**(i)** Express 49 as the sum of 7 odd numbers.

**(ii)** Express 121 as the sum of 11 odd numbers.

**Solution.**

**(i)**

49 (= \({ 7 }^{ 2 }\))

= 1 + 3 + 5 + 7 + 9 + 11 + 13

**(ii)**

121 (= \({ 11 }^{ 2 }\))

= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21.

**Question 9.**

**How many numbers lie between squares of the following numbers ?**

**(i)** 12 and 13

**(ii)** 25 and 26

**(iii)** 99 and 100.

**Solution.**

**(i) 12 and 13**

Here, n = 12

∴ 2n = 2 x 12 = 24

So, 24 numbers lie between squares of i the numbers 12 and 13.

**(ii) 25 and 26**

Here, n = 25

∴ 2n = 2 x 25 = 50

So, 50 numbers lie between squares of the numbers 25 and 26.

**(iii) 99 and 100**

Here, n = 99

∴ 2n = 2 x 99 = 198

So, 198 numbers lie between squares of of the numbers 99 and 100.

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