Square Root of 723
2026-02-28 13:12 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-723

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 723, we need to group it as 23 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n as ‘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 23, which is the new dividend. Add the old divisor with the same number 2 + 2, we get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n x n ≤ 323. Let us consider n as 8, now 48 x 8 = 384, which is more than 323, so we take n as 7, making 47 x 7 = 329.

Step 6: Subtract 329 from 323; we realize n = 6, making 46 x 6 = 276.

Step 7: Subtracting 276 from 323, the difference is 47, and the quotient is 26.8.

Step 8: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 4700.

Step 9: The new divisor is 536, because 536 x 8 = 4288.

Step 10: Subtracting 4288 from 4700, we get the result 412.

Step 11: Now the quotient is 26.8.

Step 12: Continue doing these steps until we get two numbers after the decimal point, or continue until the remainder is zero.

So the square root of √723 is approximately 26.851.