Prove that $\mathbb Q[\sqrt[3]2]$ is a field
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
54267
Field of fractions of $\mathbb{Q}[x,y]/\langle x^2+y^2-1\rangle$
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
56420
Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
35691
$\mathbb Z[\sqrt 3]$ contains infinitely many units
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
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 $
12524
Galois group of $x^3 - 2 $ over $\mathbb Q$
32760
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
146617
A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
131971
If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.
10111
Prove or disprove that Q[√2] is a field
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?