Suppose, we need to calculate the square of a perfect number like 16, the number of subtractions performed is 4, and so, the square root … 3. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. Solution: Let us find the square root of 100 first. 1. 2. The radicand is the number or expression under the radical sign √. Finding square root using long division. We know that by the property of square numbers, if a natural number is a square number, then it has to be the sum of successive odd numbers starting from 1. The total … By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect squares or not? To find square root of 121 follow the steps given below : Here, we got the result 0 in the 11th step, so we can say that  \[\sqrt{121}\] = 11. We have already learnt the square root and cube root of a number. Finding the square root of a number by repeatedly subtracting successive odd numbers from the given square number, till you get zero is known as repeated subtraction method. Join now. For example square of 4 is 16 and square root of 16 is 4. Just as the division is the inverse operation of multiplication, the square root is the inverse operation of squaring a number. By using our site, you That number is called a perfect square. Please use ide.geeksforgeeks.org, generate link and share the link here. The square root of an even number is even and that of an odd number is odd. Write a program to print all permutations of a given string, Set in C++ Standard Template Library (STL), Write Interview Square root of a number is denoted by the symbol √ . Join now. Square Root of 81 by Repeated Subtraction. Example 1: Find square root of 225 by repeated subtraction method.Â, Here we got the result 0 in the 15th step, so the square root of 225 is 15 i.e \[\sqrt{225}\] = 15, Determine the square root of 169 by repeated subtraction method.Â, Here we got the result 0 in the 13th step, so the square root of 169 is 13 i.e \[\sqrt{169}\] = 13. We start from 100-1=99,99-3=96,96-5=91,91-7=84,84-9=75,75-11=64,64 … For Example,the square root of 4 is 2, the square root of 9 is 3 and the square root of 16 is 4 and so on. 6. Solution We need to find square root of 121 by repeated subtraction method. For Example: 9 is radicand in \[\sqrt{9}\]. Find the square root of 324 by prime factorization. Square root of 100 through repeated subtraction : (i) 100-1=99 (ii) 99-3 = 96 (iii) 96-5 = 91 (iv) 91-7 = 84 (v) 84-9 = 75 (vi) 75-11 = 64 (vii) 64-13 = 51 (viii) 51-15 = 36 (ix) 36-17 = 19 (x) 19-19 = 0 Since we have subtracted 10 times, therefore sq. Repeated Subtraction: This method involves, successful and repeated subtraction of odd numbers such as 1, 3, 5 and 7 from the number until zero is reached. We know that by the property of square numbers, if a natural number is a square number, then it has to be the sum of successive odd numbers starting from 1. Example 3: Find square root of 64 by repeated subtraction method. When a number is multiplied by itself, the product is called as a ‘Square Number’. Babylonian Method and Binary Search Approach: Refer to Square root of an integer for the approaches based on Babylonian Method and Binary Search.Repeated Subtraction Approach: Follow the steps below to solve the problem: Illustration: N = 81Step 1: 81-1=80 Step 2: 80-3=77 Step 3: 77-5=72 Step 4: 72-7=65 Step 5: 65-9=56 Step 6: 56-11=45 Step 7: 45-13=32 Step 8: 32-15=17 Step 9: 17-17=0Since, 9 odd numbers were used, hence the square root of 81 is 9. 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