What is the degree of field extension ${\mathbb Q}(\sqrt2,\sqrt[8]{2},\sqrt[16]{2})$ over $\mathbb Q$?
2026-04-22 11:35:52.1776857752
what is the degree of field extension over base field?
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Can you write that field extension as a simple extension? In fact, can you see that one particular element that you are adjoining that you have written can generate the entire extension? That element has an obvious polynomial that it satisfies, and you can show it to be irreducible using Eisenstein.