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Computational Number Theory is for explicit calculations or algorithms involving anything of interest to number theorists.

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Square root in number field

This answer is meant to answer only your second question. Claim. Let $K=\mathbb{Q}(\sqrt[3]{2})$ and $\alpha = \sqrt[3]{2}-\sqrt[3]{4} \in K$. Then there does not exist $\beta \in K$ such that $\beta^ …
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