Square Root Of A Number By Repeated Subtraction

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

Square Root by Repeated Subtraction

We know that the sum of the first n odd natural numbers is n2. 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:

  1. 121 – 1 = 120
  2. 120 – 3 = 117
  3. 117 – 5 = 112
  4. 112 – 7 = 105
  5. 105 – 9 = 96
  6. 96 – 11 = 85
  7. 85 – 13 = 72
  8. 72 – 15 = 57
  9. 57 – 17 = 40
  10. 40 – 19 = 21
  11. 21 – 21 = 0

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

Click on the linked article to learn more about square roots of decimals, and know more at byjus.com


Practise This Question

1,024 trees are planted in a grid fashion such that the number of rows is equal to the number of columns. One row and one column of trees are cut such that the number of rows and columns after cutting remain equal. Find the number of trees that were cut?