Find nth root of variable without using math operators/functions Write a program which, given two positive integers n and x, will display the n-th root of x (which is also x1/n) in decimal to an accuracy of 0.00001. The program must output the resulting number in decimal, and it must work for any two numbers n and x. The variables may be defined in the program, or they may be inputted by the user, but it must work for any two positive integers.

However:


You may not use any arithmetic operators or bitwise operators (including +, *, ^, &gt;&gt;, etc.)
You may not use any built-in math functions (such as pow(), sqr(), or add()).
No web requests; the program must be completely independent from all outside sources.


Although I tagged this code-golf, a program with more code that can do the job more than 1 second faster is better. A winning program will be faster than all the other programs by more than a second. Time differences of less than 1 second will be considered negligible. If two programs complete within a second of each other, then the one with less code wins.
JavaScript

This answer doesn't satisfy all the rules, but I'm happy that at least it works. It's valid only for integers greater than one and there's no further precision.

Note that the + and &gt; operators are used for string concatenation/comparison and the maths is behind the curtain. I hope that the ! operator doesn't count as "arithmetic" as it operates over booleans.

function f(x,n){for(a=(c=',')+Array(x),s=r=c;a&gt;s;r+=c)for(i='',s=r;i!=Array(n);i+=c)s=s.split(c).join(r);return r.slice(1).length}


And some tests:


&gt; f(125,3)
5
&gt; f(16807,5)
7
&gt; f(4782969,7)
9