Square Root of 10
By M.C. Pinto, UNILA 
Brazil
By M.C. Pinto, UNILA Brazil
The method of periodic continued fractions is one of the many ways to calculate the square root of a natural number. This method uses as denominator a repetition for fractions. This repetition can be done by a fixed number of times.
For example, by repeating 2 times the continued fraction to calculate the square root of 10, we have the following equation.
Your task is to calculate the approximate value of square root of 10 given the number N of repetitions.
The input is a natural number N (0 ≤ N ≤ 100) that indicates the quantity of denominator repetitions in the continued fraction.
The output is the approximate value of the square root with 10 decimal places.
| Input Samples | Output Samples |
|
0 |
3.0000000000 |
|
1 |
3.1666666667 |
|
5 |
3.1622776623 |