(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This question is from my text.

a)show that the splitting field of (x^4)-5 over Q is Q(5^(1/4), i).

b)show that [Q(5^(1/4), i): Q = 8].

c)what is the order of the galois group of (x^4)-5 over Q?

3. The attempt at a solution

I haven't yet thought about b) and c). For a),

edit2: I have no clue how to show this. I originally thought it would be easy simply by showing the I can rewrite the polynomial into factors t(x-c1)(x-c2), where t is some constant and the cs are the given solutions, stated in the splitting field. I couldn't do it. I still have some practicing to do, but I would love any help (if any). thanks in advance.

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# Splitting fields

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