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

By successive subtracting odd natural numbers from 100,
100 – 1 = 99 99 – 3 = 96 96 – 5 = 91 91 – 7 = 84
84 – 9 = 75 75 – 11 = 64 64 – 13 = 51 51 – 15 = 36
36 – 17 = 19 19 – 19 = 0

This successive subtraction is completed in 10 steps. Therefore √100 =10
By successive subtracting odd natural numbers from 169,

169 – 1 = 168 168 – 3 = 165 165 – 5 = 160 160 – 7 = 153
153 – 9 = 144 144 – 11 = 133 133 – 13 = 120 120 – 15 = 105
105 – 17 = 88 88 – 19 = 69 69 – 21 = 48 48 – 23 = 25
25 – 25 = 0

This successive subtraction is completed in 13 steps. Therefore √169 = 13

Class 8 Maths Chapter 6 Exercise 6.3 Solution in Video

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