Square Root of 5525
2026-02-28 08:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5525

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 5525, we need to group it as 55 and 25.

Step 2: Now we need to find n whose square is 49. We can say n as ‘7’ because 7 x 7 is lesser than or equal to 55. Now the quotient is 7, and after subtracting 49 from 55, the remainder is 6.

Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number 7 + 7 to get 14, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 14n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 14n x n ≤ 625. Let us consider n as 4, now 144 x 4 = 576.

Step 6: Subtract 625 from 576. The difference is 49, and the quotient is 74.

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 4900.

Step 8: Now we need to find the new divisor that is 148 because 1486 x 6 = 8916.

Step 9: Subtracting 8916 from 4900, we get the result 16.

Step 10: Now the quotient is 74.3.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.

So the square root of √5525 is approximately 74.306.