Understanding Proof that $\mathbb{Q} \left( \sqrt {2}\right)$ is a field.
6984
Inverting $a+b\sqrt{2}$ in the field $\Bbb Q(\sqrt{2})$
112556
When is $F(\sqrt c)$ a field?
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
155125
Every ordered field has a subfield isomorphic to $\mathbb Q$?
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
50172
Show that $\mathbb{Q}(\sqrt{2})$ is the smallest subfield of $\mathbb{C}$ that contains $\sqrt{2}$
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$