Square Root of 553
2026-02-28 13:57 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-553

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 553, we need to group it as 53 and 5.

Step 2: Now we need to find n whose square is ≤ 5. We can say n as '2' because 2 x 2 is equal to 4, which is less than 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 53, which is the new dividend. 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 the value of n such that 4n x n ≤ 153. Step 5: Let us consider n as 3, now 43 x 3 = 129

Step 6: Subtract 129 from 153, the difference is 24, 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 2400.

Step 8: Now we need to find the new divisor, which is 470, because 470 x 5 = 2350. Step 9: Subtracting 2350 from 2400, we get the result 50.

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 √553 is approximately 23.51.