Serhiy Storchaka added the comment:

What if use pow() with exactly represented degree in approximating step?

    def rootn(x, n):
        g = x**(1.0/n)
        m = 1 << (n-1).bit_length()
        if n != m:
            g = (x*g**(m-n))**(1.0/m)
        return g

Maybe it needs several iterations, because it converges slower than Newton 
approximation. But every step can be faster.

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nosy: +serhiy.storchaka

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Python tracker <rep...@bugs.python.org>
<https://bugs.python.org/issue27761>
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