Question

Match the following steps with the number that we arrive at, while finding $\sqrt{81}$ by repeated subtraction

• A. 72
• B. 56
• C. 32
• D. 0

Answer 1

Successive subtraction of odd natural numbers starting with 1 from 81 eventually gives 0.
The number of steps taken to arrive at zero is its square root, this method is called repeated subtraction.

So, for 81 it is as follows.
81 - 1 = 80
80 - 3 = 77
77 - 5 = 72
72 - 7 = 65
65 - 9 = 56
56 - 11 = 45
45 - 13 = 32
32 - 15 = 17
17 - 17 = 0
As we took 9 steps to arrive at zero, the square root of 81 is 9.

$\therefore$ We have 72 on 3rd step, 56 on 5th step, 32 on 7th step and 0 on 9th step.