Question

The number of steps required to find the square root of 225 by the method of repeated subtraction is _______.

• A. 15
• B. 13
• C. 14
• D. 16

Answer 1

The correct option is A 15

The sum of first $n$ odd natural numbers is $n^2$. This fact is used to find the square root of a number by repeated subtraction. To find the square root of 225 by repeated subtraction the steps involved are:-
1) 225 - 1 = 224
2) 224 - 3 = 221
3) 221 - 5 = 216
4) 216 - 7 = 209
5) 209 - 9 = 200
6) 200 - 11 = 189
7) 189 - 13 = 176
8) 176 - 15 = 161
9) 161 - 17 = 144
10) 144 - 19 = 125
11) 125 - 21 = 104
12) 104 - 23 = 81
13) 81 - 25 = 56
14) 56 - 27= 29
15) 29- 29 = 0
The subtraction is completed in 15 steps.
$\sqrt{225}$ = 15