What is that fastest algorithm that can calculate a lot of digits of a decimal root? For example: 10,000 digits of the 3.56th root of 60.1?
An iterative method may be as follows:
where $n$ is the root desired, $x_1$ is a guess of the root of $x$ and $x_2$ is a better guess.
The iterative method is given in the book The Art of Programming Embedded Systems by Jack G. Ganssle.