Deriving nth root

As it's more of a mathematical question than a programming question, I put it here.
How do computers calculate the nth root of a number? Is it some relatively obscure formula?
You could check the the pow source code if you want to see for yourself.
powf from the math library:
http://netmite.com/android/mydroid/bionic/libm/src/e_powf.c
There are many ways a computer can approximate a function which may result in an irrational number
Wiki shows an algorithm to find the nth-root of an integer:
http://en.wikipedia.org/wiki/Nth_root#Computing_principal_roots
They use a general power algorithm, then pass in 1/n.
a^(1/n) = exp( ln( a^(1/n)) = exp( ln(a)/n )
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