Square Root of 3625
2026-02-28 10:00 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3625

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 3625, we need to group it as 36 and 25.

Step 2: Now we need to find n whose square is 36. We can say n as ‘6’ because 6 × 6 is lesser than or equal to 36. Now the quotient is 6, and after subtracting 36 - 36, the remainder is 0.

Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number 6 + 6, we 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, we need to find the value of n.

Step 5: The next step is finding 12n × n ≤ 25. Let us consider n as 2, now 12 × 2 × 2 = 48.

Step 6: Subtract 25 from 48; the difference is -23, which means n should be 1. Now 12 × 1 = 12.

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 1300.

Step 8: Now we need to find the new divisor that is 121 because 1211 × 1 = 1211.

Step 9: Subtracting 1211 from 1300, we get the result 89.

Step 10: Now the quotient is 60.2.

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 √3625 ≈ 60.21.