Square Root of 357
2026-02-28 17:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-357

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 357, we need to group it as 57 and 3.

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

Step 3: Now let us bring down 57 which is 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 get 2n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 2n x n ≤ 257. Let us consider n as 8, now 28 x 8 = 224.

Step 6: Subtract 257 from 224, the difference is 33, and the quotient is 18.

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 3300.

Step 8: Now we need to find the new divisor that is 189 because 1899 x 9 = 1701.

Step 9: Subtracting 1701 from 3300 we get the result 1599.

Step 10: Now the quotient is 18.9.

Step 11: 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 √357 is approximately 18.89.