# Thread: quesions about radical and cyclotomic extensions

1. ## quesions about radical and cyclotomic extensions

(1) Give a example of a polynomials such that its splitting field is contained in a radical extension over but is not radical over
(2)Let and .
Find and all intermediate fields between and.
(3)Which roots of unity are contained in ,where is a square free integer?
(4)Let . what does "Solve for by radicals" mean?

Thanks for any help.