Square Root of 392
2026-02-28 11:11 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-392

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 392, we need to group it as 92 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 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 92, 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, 20n, needs to be determined by finding n.

Step 5: The next step is finding 20n × n ≤ 292. Let us consider n as 1, now 20 x 1 x 1 = 20.

Step 6: Subtract 20 from 292; the difference is 272, 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 27200.

Step 8: Now we need to find the new divisor, 398, because 398 x 7 = 2786.

Step 9: Subtracting 2786 from 27200, we get the result 442.

Step 10: Now the quotient is 19.7.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue until the remainder is zero.

So, the square root of √392 ≈ 19.80