I was wondering why if we take $\alpha, \beta \in \mathbb{Q}$ such that $\sqrt{\alpha \beta} \notin \mathbb{Q}$, then we have that the field extensions $\mathbb{Q}(\sqrt{\alpha})$ and $\mathbb{Q}(\sqrt{\beta})$ are not the same. And also, it is an iff statement? It is possible to generalise it?
2026-04-09 11:38:51.1775734731
Why $\mathbb{Q}(\sqrt{\alpha})\neq \mathbb{Q}(\sqrt{\beta})$ if $\sqrt{\alpha \beta} \notin \mathbb{Q}$?
64 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ABSTRACT-ALGEBRA
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