Square Root of 113
2026-02-28 10:55 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-113

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 113, we need to group it as 13 and 1.

Step 2: Now we need to find n whose square is less than or equal to 1. We can say n as '1' because 1 × 1 is less than or equal to 1. Now the quotient is 1, and the remainder is 0 after subtracting 1 from 1.

Step 3: Bring down 13, which is the new dividend. Add the old divisor with the same number, 1 + 1, to get 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 13. Let us consider n as 6, now 26 × 6 = 156.

Step 6: Since 156 is greater than 13, we try n as 5, so 25 × 5 = 125, which is still greater. We try n as 4, so 24 × 4 = 96, which is less than 113.

Step 7: Subtract 96 from 113 to get the difference, which is 17. The quotient is 10.6.

Step 8: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1700.

Step 9: Continue this process until you reach the desired precision. The square root of √113 is approximately 10.63.