Square Root of 534
2026-02-28 01:40 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-534

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 534, we need to group it as 34 and 5.

Step 2: Now we need to find n whose square is less than or equal to 5. We can say n is ‘2’ because 2 x 2 = 4, which is less than 5. The quotient is 2, and after subtracting 5 - 4, the remainder is 1.

Step 3: Now let us bring down 34, making it the new dividend, 134. Add the old divisor with the same number 2 + 2 to get 4, which will be our new provisional divisor.

Step 4: The new divisor will be 4 followed by a digit we need to find. We need to find n such that 4n x n ≤ 134.

Step 5: The next step is finding 4n x n ≤ 134. Let us consider n as 3, now 43 x 3 = 129.

Step 6: Subtract 134 from 129; the difference is 5, and the quotient is 23.

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 500.

Step 8: Now we need to find the new divisor, which is 461 because 461 x 1 = 461.

Step 9: Subtracting 461 from 500, we get the result 39.

Step 10: Now the quotient is 23.1. 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 √534 ≈ 23.11.