Square Root of 1071
2026-02-28 10:25 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1071

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 1071, we need to group it as 71 and 10.

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

Step 3: Bring down 71, making the new dividend 171. 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 previous divisor and a number. 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 ≤ 171. Let us consider n as 2, now 62 x 2 = 124.

Step 6: Subtract 171 from 124. The difference is 47, 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 4700.

Step 8: Now we need to find the new divisor. Trying 649 x 7 = 4543.

Step 9: Subtracting 4543 from 4700, we get the result 157.

Step 10: Now the quotient is 32.7.

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 √1071 is approximately 32.718.