Square Root of 722
2026-02-28 10:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-722

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 722, we need to group it as 22 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is ‘2’ because 2 x 2 = 4 is less than 7. Now the quotient is 2, and after subtracting 4 from 7, the remainder is 3.

Step 3: Now let us bring down 22, making the new dividend 322. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

Step 4: We now have 4n as the new divisor; we need to find n such that 4n x n is less than or equal to 322. By trying n = 6, we get 46 x 6 = 276.

Step 5: Subtract 276 from 322, getting a remainder of 46. The quotient is now 26.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down two zeroes to the dividend. Now the new dividend is 4600.

Step 7: Now we need to find the new divisor that is 268 because 2688 x 8 = 4304.

Step 8: Subtracting 4304 from 4600, we get a remainder of 296.

Step 9: Now the quotient is 26.8

Step 10: 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 √722 is approximately 26.85.