Showing that $[\mathbb{Q}(\sqrt{p},\sqrt{q}):\mathbb{Q}]=4$
27784
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
53701
Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$
622
Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
46821
Finding roots in $\mathbb{Z}_p$
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?