$F=\mathbb{Q}(\alpha_1,\alpha_2, ... , \alpha_n)$, where $\alpha_i^2 \in \mathbb{Q}$ implies $\sqrt[3]{2} \notin F$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
117789
Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
34906
Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
148876
What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
125096
Minimal polynomial of $\alpha=\sqrt 2e^\frac{2\pi i}{3}$
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
112556
When is $F(\sqrt c)$ a field?