Solution: Show (i) 402 We know that, if we subtract the remainder from the number, we get a perfect square. Here, we get the remainder 2. Therefore 2 must be subtracted from 402 to get a perfect square. \therefore402-2=400 Hence, the square root of 400 is 20. (ii) 1989 We know that, if we subtract the remainder from the number, we get a perfect square. Here, we get the remainder 53. Therefore 53must be subtracted from 1989 to get a perfect square. \therefore1989-53=1936 Hence, the square root of 1936 is 44. (iii) 3250 We know that, if we subtract the remainder from the number, we get a perfect square. Here, we get the remainder 1. Therefore 1 must be subtracted from 3250 to get a perfect square. \therefore3250-1=3249 Hence, the square root of 3249 is 57. (iv) 825 We know that, if we subtract the remainder from the number, we get a perfect square. Here, we get remainder 41. Therefore 41 must be subtracted from 825 to get a perfect square. \therefore825-41=784 Hence, the square root of 784 is 28. (v) 4000 We know that, if we subtract the remainder from the number, we get a perfect square. Here, we get the remainder 31. Therefore 31 must be subtracted from 4000 to get a perfect square. \therefore4000-31=3969 Hence, the square root of 3969 is 63. 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 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 SubtractionWe know that the sum of the first n odd natural numbers is n2. We will use this fact to find the 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:
Thus, we have subtracted consecutive odd numbers from 121 starting from 1. 0 is obtained in the 11th step. So we have √121 = 11. Video Lessons on Square Roots
Finding Square Root Through Repeated SubtractionExample 1: Find the square root of 81 using the repeated subtraction method. Solution: To find: √81 The steps to find the square root of 81 is:
Here, the result “0” is obtained in step 9. Hence, the square root of 81, √81 is 9. Example 2: Find the square root of 49 using the repeated subtraction method. Solution: To find: √49 The steps to find the square root of 49 is:
The result “0” is obtained in the 7th step. Hence, the square root of 49, √49 is 7. Practice ProblemsFind the square root for the given numbers using repeated subtraction: Click on the linked article to learn more about square roots of decimals, and know more at byjus.com
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