Square Root of 432
2026-02-28 21:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-432

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 432, we need to group it as 32 and 4.

Step 2: Now we need to find n whose square is 4. We can use n as ‘2’ because 2 x 2 is equal to 4. Now the quotient is 2, and after subtracting 4-4, the remainder is 0.

Step 3: Now let us bring down 32, which is the new dividend. Add the old divisor with the same number, 2 + 2, to get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 32. Let us consider n as 0.5, now 4 x 0.5 x 0.5 = 1

Step 6: Subtract 32 from 1. The difference is 31, and the quotient is 20.5.

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 3100.

Step 8: Now we need to find the new divisor that is 9 because 409 × 9 = 3681.

Step 9: Subtracting 3681 from 3100, we get the result -581.

Step 10: Now the quotient is 20.78.

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 √432 is approximately 20.78.