How to find integer nth roots?

Question

I want to find the greatest integer less than or equal to the kth root of n. I tried

int(n**(1/k))

But for n=125, k=3 this gives the wrong

Answer 1

Here it is in Lua using Newton-Raphson method

> function nthroot (x, n) local r = 1; for i = 1, 16 do r = (((n - 1) * r) + x / (r ^ (n -   1))) / n end return r end
> return nthroot(125,3)
5
> 

Python version

>>> def nthroot (x, n):
...     r = 1
...     for i in range(16):
...             r = (((n - 1) * r) + x / (r ** (n - 1))) / n
...     return r
... 
>>> nthroot(125,3)
5
>>>