Neat method to show that $\mathbb{Q}(2^{1/3}) \ne \mathbb{Q}(3^{1/3}) $?
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
46730
How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?
51518
Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
136894
Reference request: Clean proof of Fermat's last theorem for $n=3$.
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
55582
How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?
22767
How to prove $3^\pi>\pi^3$ using algebra or geometry?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
56420
Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
128575
Elementary proof that $3$ is a primitive root of a Fermat prime?