Find the number of steps to reduce 169 to 0 by the method of repeated subtraction.

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Solution

The correct option is C 13
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 $\sqrt{169} = 13$

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