Square Root of 5125
2026-02-28 11:01 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-5125

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 5125, we need to group it as 51 and 25.

Step 2: Now we need to find n whose square is less than or equal to 51. We can say n as '7' because 7 x 7 = 49, which is less than 51. Now the quotient is 7, and after subtracting 51 - 49, the remainder is 2.

Step 3: Now let us bring down 25, making the new dividend 225. 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 ≤ 225. Let us consider n as 1; now, 14 x 1 x 1 = 14.

Step 6: Subtract 225 from 14, the difference is 211, and the quotient is 71.

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 21100.

Step 8: Now we need to find the new divisor. The closest number is 71 because 142 x 71 = 10082.

Step 9: Subtract 10082 from 21100 to get the result 11018.

Step 10: Now the quotient is 71.5.

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 √5125 ≈ 71.60.