Question

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

• A. 9
• B. 11
• C. 13
• D. 15

Answer 1

The correct option is C

13

By subtracting successive odd natural numbers from 169,

169 – 1 = 168 --------------1

168 – 3 = 165 --------------2

165 – 5 = 160 --------------3

160 – 7 = 153 --------------4

153 – 9 = 144 --------------5

144 – 11 = 133 --------------6

133 – 13 = 120 --------------7

120 – 15 = 105 --------------8

105 – 17 = 88 --------------9

88 – 19 = 69 --------------10

69 – 21 = 48 --------------11

48 – 23 = 25 --------------12

25 – 25 = 0 --------------13

Number of steps required = 13

This successive subtraction is completed in 13 steps.

Therefore $\sqrt{169}=13$