Square Root of 13154
2026-02-28 01:40 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-13154

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 13154, we need to group it as 54 and 131.

Step 2: Now we need to find n whose square is less than or equal to 131. We can say n is ‘11’ because 11 x 11 = 121, which is less than 131. Now the quotient is 11, and after subtracting 121 from 131, the remainder is 10.

Step 3: Now let us bring down 54, which is the new dividend. Add 11 with itself to get 22, which will be our new divisor.

Step 4: The next step is finding n such that 22n x n is less than or equal to 1054.

Step 5: Let us consider n as 4, so 224 x 4 = 896.

Step 6: Subtract 896 from 1054, and the difference is 158, and the new quotient becomes 114.

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 15800.

Step 8: Now we need to find the new divisor. Add 4 to 224 to get 228, and find n such that 228n x n is less than or equal to 15800.

Step 9: Continue performing these steps until you get two digits after the decimal point. So the square root of √13154 is approximately 114.672.