Square Root of 4025
2026-02-28 11:50 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4025

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 4025, we need to group it as 25 and 40.

Step 2: Now we need to find n whose square is 40. We can say n as ‘6’ because 6 x 6 = 36, which is lesser than or equal to 40. Now the quotient is 6, after subtracting 40 - 36, the remainder is 4.

Step 3: Now let us bring down 25, which makes the new dividend 425. Add the old divisor (6) with itself 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, we need to find the value of n.

Step 5: The next step is finding 12n × n ≤ 425. Let us consider n as 3, now 123 x 3 = 369.

Step 6: Subtract 425 from 369; the difference is 56, and the quotient is 63.

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 5600.

Step 8: Now we need to find the new divisor that is 634 because 6344 x 4 = 25376.

Step 9: Subtracting 25376 from 56000, we get the result 30624.

Step 10: Now the quotient is 63.4.

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 √4025 is approximately 63.47.