# Abstract Algebra elementary question

Let $F = \mathbb{Q}(\pi^3)$. How can we find a basis for $F(\pi)$ over $F$ ?

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let me know if another hint is needed –  Belgi Dec 4 '12 at 10:56

Well, as a good hint I'd say that $\,\pi\,$ is a root of $\,f(x):=x^3-\pi^3\in\Bbb Q(\pi^3)[x]=:\Bbb F[x]\,$ , and from here $\,[\Bbb F(\pi):\Bbb F]\leq 3\,$...