# NCERT Solutions For Class 8 Maths Chapter – 6 Squares and square roots Exercise – 6.1

Q1. What will be the unit digit of the squares of the following numbers ?

• 81

Solution:-

The unit  digit of a square of a number having digit 1 as unit place is 1.

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

• 272

Solution:-

The unit digit of the square of a number having digit 2 as unit place is 4

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

• 799

Solution:-

The unit digit of the square of a number having digit 9 as unit place

is 1.

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

• 3853

Solution:-

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

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

• 1234

Solution:-

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

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

Solution:-

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

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

• 52698

Solution:-

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

Unity digit of the square of number 52698 is equal to 4.

• 99880

Solution:-

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

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

• 12796

Solution:-

The unit digit of the square of a number having digit 5 as unit place is 6.

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

• 55555

Solution:-

The unit digit of the square of number having digit 5 as unit place is 5.

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

Q2. The following numbers are obviously not perfect squares. Give reason.

• 1057

Solution:-

Ends with 7.

• 23453

Solution:-

Ends with 3.

• 7928

Solution:-

Ends with 8.

• 222222

Solution:-

Ends with 2.

• 64000

Solution:-

Ends with 0

• 89722

Solution:-

Ends with 2.

• 222000

Solution:-

Ends with 0.

• 505050

Solution:-

Ends with 0.

Q3. The squares of which of the following would be odd numbers ?

• 431

Solution:-

The squares of 431 is an odd number.

• 2826

Solution:-

The squares of 2826 is an even number.

• 7779

Solution:-

The squares of 7779 is an odd number.

• 82004

Solution:-

The squares of 82004 is an even number.

Q4. Observe the following pattern and find the missing numbers. 112 = 121

1012 = 10201

10012 = 1002001

1000012 = 1……….2………1

100000012 = ……………….

Solution:-

We observe that the squares on the number on R.H.S of the equality has an odd number of digits such that the first and last digits both are 1. And , the square is symmetric about the middle digit. If the middle digit is 4 , then the number to be squared is 10101  and it s square is 102030201.

So, 10101012 = 1020304030201

1010101012 = 10203040505030201

Q6. Using the given pattern, find the missing numbers.

12 + 22 + 22 = 32

2+ 32 + 62 = 72

32 + 42 + 122 = 132

42 + 52 + 2 = 212

5 + _____2 + 302 = 312

6 + 7 + ______2 = _____2

Solution:-

Given, 12 + 22 + 2 = 32

1. e 12 + 22 + ( 1 x 2 )2 = ( 12 + 22 – 1 x 2 )2

22 + 32 + 62 = 72

ATQ    22 + 32 + (2 x 3)2 = (22 + 32 -2 x 3)2

32 + 42 + ( 3 x 4 )2 = ( 32 + 42 -3 x 4)2

42 + 52 + 202 = 212

52 + 62 + 302 = 312

62  + 72  + 422  = 432

Q7. without adding , find the sum .

1. 1 + 3 + 5 + 7 + 9

Solution:-

Sum of first five odd numbers = (5)2 = 25

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

Solution:-

Sum of first ten odd number = (10)2 = 100

• 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Solution:-

Sum of first thirteen odd number = (12)2 =144

Q8. (i.) express 49 as the sum of 7 odd numbers.

Solution:-

We know sum of first n odd naturals numbers is n2. since  , 49 = 72

ATQ: 49= sum of first 7 odd natural numbers = 1  + 3 + 5 + 7 + 9 + 11 + 13

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

Solution:-

Since ,121 = 112

ATQ: 121 = sum of first 11 odd natural numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

Q9. how many numbers lie between squares of the following numbers ?

• 12 and 13

Solution:-

12 and 13 there are  2 x 12 = 24 natural numbers

• 25 and 26

Solution:-

25 and 26 there are 2 x 25 = 50 natural numbers.

• 99 and 100

Solution:-

99 and 100 there are 2 x 99 = 198  natural numbers

एकवचन बहुवचन singular – plural -in – Hindi

NCERT Solutions For Class 8 Maths Chapter – 6 Squares and square roots Exercise – 6.1 Q1. What will be the…