Square Root of 13.1
2026-02-28 09:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-13.1

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 group the numbers from right to left. In the case of 13.1, we consider it as 13.10 for easy calculation.

Step 2: Now we need to find n whose square is less than or equal to 13. We can say n is ‘3’ because 3 × 3 = 9, which is less than 13. Now the quotient is 3, after subtracting 13 - 9, the remainder is 4.

Step 3: Bring down 10 to make the new dividend 40. Add the old divisor with the same number (3 + 3 = 6) to get the new divisor.

Step 4: The new divisor is now 6n. We need to find a value of n such that 6n × n ≤ 40. Let us consider n as 6, now 66 × 6 = 396.

Step 5: Subtract 40 from 36, the difference is 4, and the quotient is 3.6.

Step 6: 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. The new dividend is 400.

Step 7: Find the new divisor, which is 72 because 72 × 5 = 360.

Step 8: Subtract 360 from 400 to get the result 40.

Step 9: The quotient is 3.61, continue these steps until we get two numbers after the decimal point. If no decimal values exist, continue until the remainder is zero.

So the square root of √13.1 is approximately 3.619.