Square Root of 393
2026-02-28 11:17 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-393

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 393, we need to group it as 93 and 3.

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

Step 3: Now let us bring down 93, making the new dividend 293. Add the old divisor with the same number, 1 + 1, which gives us 2 as the new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 293. Let us consider n as 9, now 29 × 9 = 261.

Step 6: Subtract 261 from 293, and the difference is 32. The quotient is 19.

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 3200.

Step 8: Now we need to find the new divisor, which is 398, because 398 × 8 = 3184.

Step 9: Subtracting 3184 from 3200, we get the result 16.

Step 10: Now the quotient is 19.8.

Step 11: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √393 ≈ 19.82.