Square Root of 4725
2026-02-28 01:45 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4725

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 4725, we need to group it as 25 and 47.

Step 2: Now we need to find n whose square is closest to 47. We can say n is ‘6’ because 6 x 6 = 36, which is less than 47. The quotient is 6, and after subtracting 36 from 47, the remainder is 11.

Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number, 6 + 6, to get 12, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, where n needs to be found.

Step 5: The next step is finding 12n x n ≤ 1125. Let us consider n as 9, now 12 x 9 x 9 = 1089.

Step 6: Subtract 1125 from 1089; the difference is 36, and the quotient is 69.

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 3600.

Step 8: Now we need to find the new divisor, which is 138 because 138 x 2 = 276.

Step 9: Subtracting 276 from 3600, we get the result 324.

Step 10: Now the quotient is 68.72.

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 √4725 ≈ 68.726.