Square Root of 11600
2026-02-28 19:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-11600

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 11600, we need to group it as 00 and 116.

Step 2: Now we need to find n whose square is less than or equal to 116. We can say n is 10 because 10 x 10 = 100, which is lesser than 116. The quotient is 10, and the remainder is 116 - 100 = 16.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 10 + 10 to get 20, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 20n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 20n x n ≤ 1600. Let us consider n as 8; now 208 x 8 = 1664, which is more than 1600, so n is 7.

Step 6: Subtract 1600 from 207 x 7 = 1449, the difference is 151, and the quotient is 107.

Step 7: 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 15100.

Step 8: Now we need to find the new divisor, which is 215, because 215 x 7 = 1505.

Step 9: Subtracting 1505 from 15100, we get the result 595.

Step 10: Now the quotient is 107.7.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √11600 is 107.70