yes, it is in the first way a math question.
I have drawn up an algorithm myself because I have not found such an algorithm on the net.
Granted, there may be faster algorithms out there, but a solution on my computer took only 1 millisecond for a 20th root of a 10^80 biginteger, which isn't bad.
I also found an idea on the net, but I didn't develop it
It is based on (a+b)^n = a^n + nba^(n-1) + ..... +b^n where a is a temporary solution and b is the improvement to be made.
b is determined approximately with (a+b)^n = a^n + nba^(n-1) and so on proceed in the same way.
I think this is faster.