I need to show that $\sqrt[7]{2}\not\in\mathbb{Q}(\sqrt[7]{3})$ but I have no idea how to do it. I've tried to reason with the extension degrees but I haven't got any satisfactory result.
Could someone help me?
Thanks in advance.
2026-04-29 19:17:38.1777490258
Prove that $\sqrt[7]{2}\not\in\mathbb{Q}(\sqrt[7]{3})$
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