Square Root of 323
2026-02-28 11:36 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-323

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square numbers 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 323, we group it as 23 and 3.

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

Step 3: Now let us bring down 23, which becomes the new dividend. Add the old divisor with the same number 1 + 1, we get 2, which will be our new divisor.

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

Step 5: The next step is finding 2n x n ≤ 223. Let us consider n as 8; now 28 x 8 = 224.

Step 6: Since 28 x 8 = 224 is greater than 223, check 27 x 7 = 189. Subtract 189 from 223; the difference is 34, and the quotient is 17.

Step 7: Since the remainder is less than the divisor, add a decimal point, allowing us to append two zeroes to the dividend. Now the new dividend is 3400.

Step 8: Find the new divisor, which is 179 because 179 x 9 = 1611.

Step 9: Subtracting 1611 from 3400 gives the result 1789.

Step 10: Now the quotient is approximately 17.9.

Step 11: Continue these steps until reaching a desired level of precision or until the remainder is zero.

So the square root of √323 is approximately 17.972.