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

How about:

def nth_root(val, n):
    ret = int(val**(1./n))
    return ret + 1 if (ret + 1) ** n == val else ret

print nth_root(124, 3)
print nth_root(125, 3)
print nth_root(126, 3)
print nth_root(1, 100)

Here, both val and n are expected to be integer and positive. This makes the return expression rely exclusively on integer arithmetic, eliminating any possibility of rounding errors.

Note that accuracy is only guaranteed when val**(1./n) is fairly small. Once the result of that expression deviates from the true answer by more than 1, the method will no longer give the correct answer (it'll give the same approximate answer as your original version).

Still I am wondering why int(125**(1/3)) is 4

In [1]: '%.20f' % 125**(1./3)
Out[1]: '4.99999999999999911182'

int() truncates that to 4.