Showing $\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$.
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
50668
Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
46730
How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?
19525
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
21155
Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
4228
Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$