Square Root of 3725
2026-02-28 08:33 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3725

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 3725, we can group it as 37 and 25.

Step 2: Now we need to find n whose square is less than or equal to 37. We can say n is 6 because 6 x 6 = 36, which is less than 37. Now the quotient is 6, and after subtracting 36 from 37, the remainder is 1.

Step 3: Bring down the next pair of numbers, which is 25, making the new dividend 125.

Step 4: Add the old divisor with the same number 6 + 6 = 12, which will be part of our new divisor.

Step 5: The next step is finding 12n × n ≤ 125. Let us consider n as 1, now 121 x 1 = 121, which is less than 125.

Step 6: Subtract 121 from 125; the difference is 4. The quotient is 61.

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 zeros to the dividend. Now the new dividend is 400.

Step 8: Now we need to find the new divisor that is 122 because 1223 x 3 = 366

Step 9: Subtracting 366 from 400, we get the result 34.

Step 10: Now the quotient is 61.0.

Step 11: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √3725 is approximately 61.05.