Let $\mathbb{Q}[\sqrt{2}] = $ {$a + b \sqrt{2}$ | $a, b \in \mathbb{Q} $}. Prove that $\mathbb{Q}[\sqrt{2}]$ is a subfield of $\mathbb{C}$
63280
Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.
10111
Prove or disprove that Q[√2] is a field
136770
Any field that contains the integers contains the rationals as a subfield (Analysis proof)
22158
Find the quadratic sub field of $\mathbb Q(\zeta_7)$ which can be expressed in the form $\mathbb Q(\sqrt D)$,where $D$ is an integer.
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
27021
Show that $Q[\sqrt3]$ is a field
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
95459
$\mathbb{Q}(\sqrt{2+\sqrt{2}})$ is Galois over $\mathbb{Q}$?
62183
Find the quotient field of $\mathbb{Z}[\sqrt {2}]$
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
114152
Intermediate fields between $\mathbb{Z}_2 (\sqrt{x},\sqrt{y})$ and $\mathbb{Z}_2 (x,y)$
4228
Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
34906
Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.