The DAV Class 8 Maths Book Solutions and **DAV Class 8 Maths Chapter 1 Worksheet 2** Solutions of Squares and Square Roots offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 1 WS 2 Solutions

Find the square root of the following numbers by the repeated subtraction method.

Question 1.

16

Solution:

\(\sqrt{16}\)

(i) 16 – 1 = 15

(ii) 15 – 3 = 12

(iii) 12 – 5 = 7

(iv) 7 – 7 = 0

We have subtracted the successive odd numbers from 16 and obtained 0 in the forth step.

∴ \(\sqrt{16}\) = 4

Question 2.

49

Solution:

\(\sqrt{49}\)

(i) 49 – 1 = 48

(ii) 48 – 3 = 45

(iii) 45 – 5 = 40

(iv) 40 – 7 = 33

(v) 33 – 9 = 24

(vi) 24 – 11 = 13

(vii) 13 – 13 = 0

We have subtracted the successive odd numbers from 49 and obtained 0 in the seventh step.

∴ \(\sqrt{49}\) = 7

Question 3.

64

Solution:

\(\sqrt{64}\)

(i) 64 – 1 = 63

(ii) 63 – 3 = 60

(iii) 60 – 5 = 55

(iv) 55 – 7 = 48

(v) 48 – 9 = 39

(vi) 39 – 11 = 28

(vii) 28 – 13 = 15

(viii) 15 – 15 = 0

We have subtracted the successive odd numbers from 64 and obtained 0 in the eighth step.

∴ \(\sqrt{64}\) = 8

Question 4.

100

Solution.

\(\sqrt{100}\)

(i) 100 – 1 = 99

(ii) 99 – 3 = 96

(iii) 96 – 5 = 91

(iv) 91 – 7 = 84

GO 84 – 9 = 75

(vi) 75 – 11 = 64

(vii) 64 – 13 = 51

(viii) 51 – 15 = 36

(ix) 36 – 17 = 19

(x) 19 – 19 = 0

We have subtracted the successive odd numbers from 100 and obtained 0 in the tenth step.

∴ \(\sqrt{100}\) = 10

Question 5.

169

Solution:

\(\sqrt{169}\)

CD 169 – 1 = 168

(ii) 168 – 3 = 165

(iii) 165 – 5 = 160

(iv) 160 – 7 = 153

(v) 153 – 9 = 144

(vi) 144 – 11 = 133

(vii) 133 – 13 = 120

(viii) 120 – 15 = 105

(ix) 105 – 17 = 88

(x) 88 – 19 = 69

(xi) 69 – 21 = 48

(xii) 48 – 23 = 25

(xiii) 25 – 25 = 0

We have subtracted successive odd numbers from 169 and obtained 0 in the thirteenth step.

∴ \(\sqrt{169}\) = 13

Question 6.

81

Solution:

\(\sqrt{81}\)

(i) 81 – 1 = 80

(ii) 80 – 3 = 77

(iii) 77-5 = 72

(iv) 72 – 7 = 65

(v) 65 – 9 = 56

(vi) 56 – 11 = 45

(vii) 45 – 13 = 32

(viii) 32 – 15 = 17

(ix) 17 – 17 = 0

We have subtracted successive odd natural numbers from 81 and obtained 0 in the ninth step.

∴ \(\sqrt{81}\) = 9.

Question 7.

256

Solution:

\(\sqrt{256}\)

(i) 256 – 1 = 255

(ii) 255 – 3 = 252

(iii) 252 – 5 = 247

(iv) 247 – 7 = 240

(v) 240 – 9 = 231

(vi) 231 – 11 = 220

(vii) 220 – 13 = 207

(viii) 207 – 15 = 192

(ix) 192 – 17 = 175

(x) 175 – 19 = 156

(xi) 156 – 13 = 135

(xii) 135 – 15 = 112

(xiii) 112 – 25 = 87

(xiv) 87 – 27 = 60

(xv) 60 – 29 = 31

(xvi) 31 – 31 = 0

We have subtracted successive odd natural numbers from 256 and obtained 0 in the sixteenth step.

∴ \(\sqrt{256}\) = 16.

Question 8.

144

Solution:

\(\sqrt{144}\)

1. 144 – 1 = 143

2. 143 – 3 = 140

3. 140 – 5 = 135

4. 135 – 7 = 128

5. 128 – 9 = 119

6. 119 – 11 = 108

7. 108 – 13 = 95

8. 95 – 15 = 80

9. 80 – 17 = 63

10. 63 – 19 = 44

11. 44 – 21 = 23

12. 23 – 23 = 0

We have subtracted successive odd natural numbers from 144 and obtained 0 in the twelfth step.

∴ \(\sqrt{144}\) = 12.

### DAV Class 8 Maths Chapter 1 Worksheet 2 Notes

- The square root of an odd number is odd.
- The square root of an even number is even.
- The symbol of square root is √ or raised to the power
- If m is a square root of n, then n is the square of m.

**Methods to find the Square Roots:**

(i) Repeated Subtraction Method

Example 1.

Find \(\sqrt{49}\) by repeated subtraction method.

Solution:

(i) 49 – 1 = 48

(ii) 48 – 3 = 45

(iii)45 – 5 = 40

(iv) 40 – 7 = 33

(u) 33 – 9 = 24

(vi) 24 – 11 = 13

(vii) 13 – 13 = 0

We have subtracted the successive odd number 1,3, 5, 7, 9, 11 and 13 and got 0 in the seventh step.

∴ \(\sqrt{49}\) = 7.

Example 2.

Find the square root of 81 by repeated subtraction method.

Solution:

(i) 81 – 1 = 80

(ii) 80 – 3 = 77

(iii) 77 – 5 = 72

(iv) 72 – 7 = 65

(v) 65 – 9 = 56

(vi) 56 – 11 = 45

(vii) 45 – 13 = 32

(viii) 32 – 15 = 17

(ix) 17 – 17 = 0

We have subtracted the successive odd number and obtained 0 in the ninth step.

∴ \(\sqrt{81}\) = 9.