Square Root of 386
2026-02-28 17:49 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-386

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 386, we need to group it as 86 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 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 86, making the new dividend 286. Add the old divisor with the same number, 1 + 1, giving us 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, and we need to find the value of n.

Step 5: Finding 2n × n ≤ 286, let us consider n as 9, then 2 x 9 x 9 = 261.

Step 6: Subtract 261 from 286, the difference is 25, and the quotient becomes 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. The new dividend is 2500.

Step 8: Find the new divisor, which is 193 because 1939 x 9 = 17451.

Step 9: Subtracting 17451 from 25000, we get the result 7549.

Step 10: Now the quotient is approximately 19.6.

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 √386 is approximately 19.65.