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 $t^{1/3}$ were a polynomial, then its degree would be at least one (because it is not constant). This would imply 
$$
\lim_{t\to\infty}\frac{t^{1/3}}t\ne0.
$$
But, precisely, the limit above is indeed zero. So $t^{1/3}$ cannot be a polynomial. 
