Question: It is a fact, which we can verify by cubing, that the zeros of x 3 - 2 in Q are where 3 2, as

It is a fact, which we can verify by cubing, that the zeros of x3 - 2 in Q are

a = 32, -1+i3 2 / = 3/2= and 3 = 32.


where 3√2, as usual, is the real cube root of 2.

Describe all extensions of the automorphism ψ√3,-√3 of Q(√3) to an isomorphism mapping Q(i, √3, 3√2) onto a subfield of Q̅.

a = 32, -1+i3 2 / = 3/2= and 3 = 32. . -1-i3 2

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