Question

Find the number of steps required to find the square root of 169 by repeated subtraction method.

• A. 9
• B. 11
• C. 13
• D. 15

Answer 1

The correct option is C 13

We know that the sum of consecutive odd numbers gives a square number.

If we subtract the consecutive odd numbers from the given square number, we will eventually get 0.

The number of steps taken to get 0 is equal to the square root of the given number.

Successive subtraction of odd natural numbers from 169, is as follows:

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.

$\therefore \sqrt{169}=13$