Square Root of 425
2026-02-28 21:46 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-425

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 425, we need to group it as 25 and 4.

Step 2: Now we need to find n whose square is ≤ 4. We can say n is '2' because 2 x 2 = 4. Now the quotient is 2, and after subtracting, 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 2 + 2, we get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n x n ≤ 25. Let us consider n as 5, now 4 x 5 x 5 = 100.

Step 6: Subtract 25 from 100, and the difference is -75, but since 100 exceeds, n needs to be less, so calculate again.

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 2500.

Step 8: Now we need to find the new divisor that is 41 because 415 x 5 = 2075.

Step 9: Subtracting 2075 from 2500, we get the result 425.

Step 10: Now the quotient is 20.5.

Step 11: Continue doing these steps until we get two numbers after the decimal point. If there is no decimal value, continue until the remainder is zero.

So the square root of √425 is approximately 20.6155.