I am convinced that the splitting field over ${\mathbb Q}$ of $f(t)=t^6-10t^3+22$ has degree 36. This is equivalent to prove that $\sqrt[3]{5+\sqrt{3}}$ does not belong to ${\mathbb Q}(\sqrt[3]{5-\sqrt{3}})$ and I am not able to check this. Could anyone help to me?
2026-05-04 12:25:32.1777897532
Splitting field of a polynomial of degree 6
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