How to determine galois group?

I have trouble in determining Galois group.
Can anyone help me with the following question:

how to determine the Galois group of (x^2-2)(x^2-3)(x^2-5), determine all the subfields of the splitting field of this polynomial?

how to determine the elements of the galois group of x^p-2 for p is prime.

Thanks a lot!
 

HallsofIvy

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The set of solutions of xp= a are of the form [itex]|a|^{1/p}\omega^i[/itex] with i ranging from 0 to p-1, where [itex]\omega[/itex] is the "principal pth root of unity". The Galois group is the permutation group of that set: the permutation group on p objects.
 

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