Square Root of 92
2026-02-28 13:44 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-92

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 92, we treat it as 92.

Step 2: Now we need to find n whose square is less than or equal to 9. We can say n is 3 because 3 x 3 = 9. Now the quotient is 3, after subtracting 9 from 9, the remainder is 0.

Step 3: Now let us bring down 2, which is the new dividend. Add the old divisor with the same number, 3 + 3 we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 92. Suppose n as 1, then 6 x 1 = 6, 60 + 1 = 61.

Step 6: Subtract 61 from 92, the difference is 31, and the quotient is 9.

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 3100.

Step 8: Now we need to find the new divisor, which is 96 because 961 x 3 = 2883.

Step 9: Subtracting 2883 from 3100, we get 217.

Step 10: Now the quotient is 9.5.

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 √92 is approximately 9.59.