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## Homework Statement

I have the field [tex] F_5 [/tex] and I adjoin some square root of 2 , say [tex]2^{1/4}[/tex]. Is there a way to see that the multiplicative group inside [tex]F_5(2^{1/4})[/tex] is cyclic and find the generator?

## Homework Equations

## The Attempt at a Solution

I did the [tex]F_5(2^{1/2})[/tex] case and think the generator is [tex]2+\sqrt{2}[/tex]. But don't know how this generalizes..

Thanks!