It is a fact, which we can verify by cubing, that the zeros of x 3 -

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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 identity map of Q to an isomorphism mapping Q(3√2, √3) onto a subfield of Q̅.

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