nth root algorithm: value of initial guess?

Question

I wonder what value one would choose to maximize efficiency to make an initial guess for the nth root algorithm (supplementary constraint: only with the five operations: +, -, *, /, % (integer modulo)) presented here on wikipedia: http://en.wikipedia.org/wiki/Nth_root_algorithm

Answer 1

You want to be as close as possible, so it depends on how you get the number to take the $n^{\text{th}}$ root of. If it is a floating point computer number, you have an exponent, so divide it by $n$. In mathematical theory, no number is better than any other. But in real life numbers tend to be around $1$ in magnitude, so without other information I would start there.