Square Root of 6725
2026-02-28 17:59 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-6725

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 6725, we need to group it as 67 and 25.

Step 2: Now we need to find n whose square is 67. We can say n as ‘8’ because 8 × 8 is 64, which is lesser than or equal to 67. Now the quotient is 8; after subtracting 64 from 67, 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: 8 + 8 = 16, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 16n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 16n × n ≤ 325. Let us consider n as 2; now 16 × 2 × 2 = 64.

Step 6: Subtract 64 from 325, and the difference is 261. The quotient is 82.

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 26100.

Step 8: Now we need to find the new divisor that is 164, because 1640 × 1 = 1640.

Step 9: Subtracting 1640 from 26100, we get the result 10460.

Step 10: Now the quotient is 82.0

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 √6725 is approximately 82.007.