Square Root of 5225
2026-02-28 11:54 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5225

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 5225, we need to group it as 25 and 52.

Step 2: Now we need to find n whose square is close to 52. We can say n is ‘7’ because 7 x 7 is 49, which is less than 52. Now the quotient is 7, and after subtracting 49 from 52, the remainder is 3.

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

Step 4: The new divisor will be in the form of 14n. Now we need to find the value of n.

Step 5: The next step is finding 14n x n ≤ 325. Let us consider n as 2; now 14 x 2 x 2 = 284.

Step 6: Subtract 284 from 325; the difference is 41, and the quotient is 72.

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 4100.

Step 8: Now we need to find the new divisor, which is 723, because 723 x 3 = 2169.

Step 9: Subtracting 2169 from 4100, we get the result 1931.

Step 10: Now the quotient is 72.3.

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

So the square root of √5225 is approximately 72.30.