How to prove that $n^{\frac{1}{3}}$ is not a polynomial? I'm reading Barbeau's Polynomials, there's an exercise:

How to prove that $n^{\frac{1}{3}}$ is not a polynomial?

I've made this question and with the first answer as an example, I guess I should assume that:
$$n^{\frac{1}{3}}=a_pn^p+a_{p-1}n^{p-1}+\cdots+ a_0n^0$$
And then I should make some kind of operation in both sides, the resultant difference would be the proof. But I have no idea on what operation I should do in order to prove that. 

If $t^{1/3}$ is a polynomial, then its derivative $\frac{1}{3}t^{-2/3}$ also is. But it's clearly impossible (for example it would not be continuous at $0$).
