Quick way of showing $[\mathbb{Q}(\sqrt[4]2,\sqrt3):\mathbb{Q}]=8$?
34906
Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
114295
Find all the middle fields of the splitting field of $x^4-2$ over $\mathbb{Q}$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
157496
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
95602
Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $
50668
Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
62183
Find the quotient field of $\mathbb{Z}[\sqrt {2}]$
21155
Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
622
Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
6837
How to quotient $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$?