NCERT Solutions For Class 8, Maths, Chapter 6, Squares And Square Roots, Exercise 6.3

Q.3. Find the square roots of 100 and 169 by the method of repeated subtraction.

Ans:

(1) The square root of 100 can be obtained by the method of repeated subtraction as:

(i) 100 – 1 = 99

(ii) 99 – 3 = 96

(iii) 96 – 5 = 91

(iv) 91 – 7 = 84

(v) 84 – 9 = 75

(vi) 75 – 11= 64

(vii) 64 – 13 = 51

(viii) 51 – 15 = 36

(ix) 36 – 17 = 19

(x) 19 – 19 = 0

Here, we obtained 0 at 10^th step

Therefore, $\sqrt{\mathsf{100}}\mathsf{=10}$

(2) The square root of 169 can be obtained by the method of repeated subtraction as:

(i) 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

Here, we obtained 0 at 13^th step

Hence,        $\sqrt{\mathsf{169}}\mathsf{=13}$