Square Root of 368
2026-02-28 13:28 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-368

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 368, we need to group it as 68 and 3.

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

Step 3: Now let us bring down 68, 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 20 (2n), and we need to find a number n such that 20n x n ≤ 268.

Step 5: Consider n as 9, then 209 x 9 = 1881, which is less than 2680, so n = 9.

Step 6: Subtract 1881 from 2680, the difference is 799, and 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 79900.

Step 8: Now we need to find the new divisor that is 193 because 1939 x 9 = 17451.

Step 9: Subtracting 17451 from 79900, we get the result 62449.

Step 10: Now the quotient is 19.1

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 √368 ≈ 19.18