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- Jan 26, 2012

- 995

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**: Let $F$ be a field of characteristic not equal to $2$. State and prove a necessary and sufficient condition on $\alpha, \beta \in F$ so that $F(\sqrt{\alpha})=F(\sqrt{\beta})$. Use this to determine whether $\mathbb{Q}(\sqrt{1-\sqrt{2}})=\mathbb{Q}(i, \sqrt{2}).$**

Problem

Problem

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