Square Root of 191
2026-02-28 17:27 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-191

The long division method is particularly used for non-perfect square numbers. In this method, we should find 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 191, we need to group it as 91 and 1.

Step 2: Now we need to find n whose square is less than or equal to 1. We can say n is '1' because 1 × 1 is less than or equal to 1. Now the quotient is 1; after subtracting 1 - 1, the remainder is 0.

Step 3: Now let us bring down 91, which is the new dividend. Add the old divisor with the same number: 1 + 1 = 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 ≤ 91. Let us consider n as 4, now 2 × 4 × 4 = 32.

Step 6: Subtract 91 from 32, the difference is 59, and the quotient is 14.

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 5900.

Step 8: Now we need to find the new divisor, which will be 289, because 289 × 9 = 2601.

Step 9: Subtracting 2601 from 5900, we get the result 3299.

Step 10: Now the quotient is 13.8.

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 √191 is approximately 13.82.