Square Root of 493
2026-02-28 10:24 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-493

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, we need to group the numbers from right to left. In the case of 493, we consider 93 and 4.

Step 2: Now we need to find n whose square is less than or equal to 4. We can say n is 2 because 2 x 2 = 4. Now the quotient is 2, and after subtracting 4, the remainder is 0.

Step 3: Bring down 93, which is the new dividend. Add the old divisor with the same number (2), and we get 4, which will be our new divisor.

Step 4: The new divisor will be the sum of the previous divisor and quotient. We need to find n such that 4n x n ≤ 93.

Step 5: Consider n as 2, then 42 x 2 = 84.

Step 6: Subtract 84 from 93, the difference is 9, and the quotient is 22.

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 900.

Step 8: Find the new divisor, which is 445 because 445 x 2 = 890.

Step 9: Subtracting 890 from 900, we get the result 10.

Step 10: Now the quotient is 22.2.

Step 11: Continue 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 √493 is approximately 22.205.