You have already learned about the squares and cubes of a number. 1, 4, 9, 16, 25, etc. are the squares of the numbers 1, 2, 3, 4, 5 and so on. In the series 1, 4, 9…, the numbers are called** perfect squares** or square numbers. Thus, a square number can be defined as an integer that can be expressed as a product of a number with the number itself. And the number which is multiplied with itself, is called the **square root** of the square number. So 25 is a square number that can be written as 5 X 5. And 5 is the square root of 25. Now finding the square of a number is simple. You multiply 10 with 10 and you obtain 100, which is the square of 10. But how do you go about finding the square root of a number? There are several methods for the same. In this article, we will learn how to find the square root of a number through repeated subtraction.

Square Root by Repeated Subtraction

We know that the sum of the first *n* odd natural numbers is *n ^{2}*. We will use this fact to find square root of a number by repeated subtraction. Let us take an example to learn this method. Say, you are required to find the square root of 121, that is, √121. The steps are:

- 121 – 1 = 120
- 120 – 3 = 117
- 117 – 5 = 112
- 112 – 7 = 105
- 105 – 9 = 96
- 96 – 11 = 85
- 85 – 13 = 72
- 72 – 15 = 57
- 57 – 17 = 40
- 40 – 19 = 21
- 21 – 21 = 0

Thus, we have subtracted consecutive odd numbers from 121 starting from 1. 0 is obtained in the 11^{th} step. So we have √121 = 11.

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