(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Splitting fields

**Physics Forums | Science Articles, Homework Help, Discussion**