Square Root of 391
2026-02-28 08:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-391

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 391, we need to group it as 91 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 × 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 91, 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 × n ≤ 291. Let us consider n as 7, now 27 × 7 = 189.

Step 6: Subtract 189 from 291, the difference is 102, and the quotient is 17.

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 10200.

Step 8: Now we need to find the new divisor that is 197 because 197 × 5 = 985.

Step 9: Subtracting 985 from 10200, we get the result 215.

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 are no decimal values, continue till the remainder is zero.

So the square root of √391 is approximately 19.77.