Square Root of 355
2026-02-28 10:19 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-355

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 355, we need to group it as 55 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 x 1 from 3 leaves a remainder of 2.

Step 3: Now let us bring down 55, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.

Step 4: The new divisor will be 2n. We need to find the value of n such that 2n x n ≤ 255. Let us consider n as 8, so 28 x 8 = 224.

Step 5: Subtract 224 from 255; the difference is 31, and the quotient is 18.

Step 6: 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 3100.

Step 7: Now we need to find the new divisor, which is 189 because 189 x 9 = 1701.

Step 8: Subtracting 1701 from 3100 gives us the result 1399.

Step 9: Now the quotient is 18.8.

Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √355 is approximately 18.84.