Table of Contents
- Finding Square Root by Repeated Subtraction
- What’s Next?
In the previous segment, we learnt what a Square root is. In this segment, we will learn how to find the square root using repeated subtraction.
How to find square root by repeated subtraction method?
We know that a square number can be expressed as the sum of successive odd natural numbers starting with 1.
For example, 25 = 1 + 3 + 5 + 7 + 9
This means we can find out the square root of a perfect square number by repeated subtraction of successive odd numbers from it, starting with 1.
Let’s understand this better by finding the square root of 81.
Starting with 1, let us subtract consecutive odd numbers successively till we reach 0. 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
On reaching the number zero, count the total number of steps that were required. In this case, 9 steps were needed. That is we reached 0 in the 9th step.
This means, f we add 9 successive odd numbers starting from 1 we get the number 81. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
Hence we can say that, 92 = 81
In other words, √81 = 9
Related content
| Square Roots of Decimals |
| Finding the Square of a Number |
