$Q⊂L$ is a field extension with $ [L : Q] = 32$. Show that 2 is not a third power in $L$.

Question

Suppose that $Q⊂L$ is a field extension with $ [L : Q] = 32$. We have to show that 2 is not a third power in $L$.

My try:Actually I could not understand what is required to show .Please help in understanding this one.Thank you.

Answer 1

If $\alpha\in L$ such that $\alpha^3=2$, then $[Q(\alpha):Q]=3$.What can you say about [L:Q] now?