# Math Help - normal extension of the rationals - quick questions

1. ## normal extension of the rationals - quick questions

Just trying to get my head around normal extensions.

True or False?

is a normal extension of

is a normal extension of

I would say for the first one, true, because it is the splitting field of .

For the second one, false, because is irreducible by Eisenstein, and has only one zero > 0 in

Could anyone please tell me if these are OK?

You can tell the second is not normal because the other two roots are imaginary and $\mathbb{Q}(2^{1/3})\subset \mathbb{R}$. But yeah I think you got it.