Square Root of 564
2026-02-28 17:58 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-564

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 564, we need to group it as 64 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 is lesser than or equal to 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 64, making the new dividend 164. Add the old divisor with the same number, 2 + 2, we get 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find n such that 4n x n ≤ 164. Let us consider n as 3, now 43 x 3 = 129.

Step 5: Subtract 129 from 164, the difference is 35, and the quotient is 23.

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. Now the new dividend is 3500.

Step 7: Now we need to find the new divisor, which is 474 because 474 x 7 = 3318.

Step 8: Subtracting 3318 from 3500, we get the result 182.

Step 9: Now the quotient is 23.7 Step 10: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √564 is approximately 23.75.