Question

To find square root of 256 by repeated subtraction method, which step is 175 and the total number of steps of subtraction is ____.

• A. 9th step, 16
• B. 9th step, 12
• C. 10th step , 12
• D. 10th step, 16

Answer 1

The correct option is A 9th step, 16

We know that the sum of first $n$ odd natural numbers is $n^2$.
Therefore, the square root of a number can be found by repeatedly subtracting odd numbers from the given number starting from 1.
So in this case,
Step 1 $\Rightarrow$ 256 - 1 = 255,
Step 2 $\Rightarrow$ 255 - 3 = 252
Step 3 $\Rightarrow$ 252 - 5 = 247
Step 4 $\Rightarrow$ 247 - 7 = 240
Step 5 $\Rightarrow$ 240 - 9 = 231
Step 6 $\Rightarrow$ 231 - 11 = 220
Step 7 $\Rightarrow$ 220 - 13 = 207
Step 8 $\Rightarrow$ 207 - 15 = 192
Step 9 $\Rightarrow$ 192 - 17 = 175
Step 10 $\Rightarrow$ 175 - 19 = 156
Step 11 $\Rightarrow$ 156 - 21 = 135
Step 12 $\Rightarrow$ 135 - 23 = 112
Step 13 $\Rightarrow$ 112 - 25 = 87
Step 14 $\Rightarrow$ 87 - 27 = 60
Step 15 $\Rightarrow$ 60 - 29 = 31
Step 16 $\Rightarrow$ 31 - 31 = 0
Here, 9th step is 175 and total number of steps of repeated subtraction is 16.