Square Root of 422
2026-02-28 11:51 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-422

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 422, we need to group it as 42 and 2.

Step 2: Now we need to find n whose square is less than or equal to 4. We can say n as ‘2’ because 2 x 2 = 4. Now the quotient is 2, and after subtracting 4 - 4, the remainder is 0.

Step 3: Now let us bring down 22, 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 ≤ 22. Let us consider n as 5, now 45 x 5 = 225, which is greater than 22. So, we consider n as 4, now 44 x 4 = 176.

Step 6: Subtract 176 from 220 (since we consider 22 as 220), the difference is 44, and the quotient is 24.

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 4400.

Step 8: Now we need to find the new divisor that is 409 because 409 x 5 = 2045

Step 9: Subtracting 2045 from 4400, we get the result 2355.

Step 10: Now the quotient is 20.5

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 √422 is approximately 20.54.