Square Root of 1076
2026-02-28 11:08 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1076

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 1076, we need to group it as 76 and 10.

Step 2: Now we need to find n whose square is 10. We can say n is ‘3’ because 3 x 3 is 9, which is less than or equal to 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.

Step 3: Now let us bring down 76 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 x n ≤ 176. Let us consider n as 2, now 6 x 2 x 2 = 144.

Step 6: Subtract 176 from 144, the difference is 32, and the quotient is 32.

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 3200.

Step 8: Now we need to find the new divisor that is 65 because 651 x 5 = 3255.

Step 9: Subtracting 3255 from 3200, we get the result -55, which indicates the approximation was slightly high.

Step 10: Now the quotient is approximately 32.79.

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

So the square root of √1076 is approximately 32.79.