Find the square roots of 100 and 169 by the method of repeated sub traction

The square root of 100 can be obtained bythe method of repeated sub traction 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

In this we have subtracted successive odd numbers starting from 1 to 100, and obtained 0 at 10th step

Therefore,

√100 = 10

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

We have subtracted successive odd numbers starting from 1 to 169, and obtained 0 at 13 th step

Hence,

√169 = 13