Square Root of 556
2026-02-28 12:42 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-556

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 556, we need to group it as 56 and 5.

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

Step 3: Now let us bring down 56, 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. We need to find the value of n such that 4n x n ≤ 156.

Step 5: The next step is finding 4n x n ≤ 156. Let us consider n as 3, now 43 x 3 = 129

Step 6: Subtract 156 from 129. The difference is 27, 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 2700.

Step 8: Now, we need to find the new divisor, which is 469 because 469 x 5 = 2345.

Step 9: Subtracting 2345 from 2700, we get the result 355.

Step 10: Now the quotient is 23.5

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 √556 is approximately 23.57.