Question

Using the repeated subtraction method, how many steps are required to find the square root of 81? Also tell what is the square root of 81?

Answer 1

We know that the sum of consecutive odd numbers gives a square number.
$1+3+5+7+9\dots \dots \dots \dots .=n^2$
If we subtract the consecutive odd numbers from the given square number, we will eventually get 0.
The number of steps taken to get 0 is equal to the square root of the given number.
Successive subtraction of odd natural numbers from 225, 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
This successive subtraction is completed in 9 steps.
So square root of 81 = 9