Square Root of 122
2026-02-21 20:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-122

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 digits of 122 from right to left.

Step 2: Now we need to find n whose square is less than or equal to 1. We can say n as ‘1’ because 1 x 1 is less than or equal to 1. Now the quotient is 1; after subtracting 1 - 1, 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, 1 + 1, to get 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 22. Let us consider n as 1; now 2 x 1 x 1 = 2

Step 6: Subtract 22 from 2; the difference is 20, and the quotient is 11

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 2000.

Step 8: Now we need to find the new divisor that is 21 because 211 x 9 = 1899

Step 9: Subtracting 1899 from 2000, we get the result 101.

Step 10: Now the quotient is 11.0

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

So, the square root of √122 ≈ 11.04