Square Root of 1072
2026-02-28 11:23 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1072

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 1072, we need to group it as 72 and 10.

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

Step 3: Now let us bring down 72, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor is 6n. We need to find the value of n such that 6n x n ≤ 172. Let us consider n as 2, now 62 x 2 = 124.

Step 5: Subtract 124 from 172; the difference is 48, and the quotient is 32.

Step 6: 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 4800.

Step 7: Now we need to find the new divisor, which is 649 because 649 x 7 = 4543.

Step 8: Subtracting 4543 from 4800, we get the result 257.

Step 9: Now the quotient is 32.7.

Step 10: 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 √1072 is approximately 32.74.