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

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.

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a₁ = 32, -1+i√3 2 α/₂ = 3/2= and α3 = 32. ܚ . -1-i√3 2