Show that $\sqrt b \in \mathbb Q(\sqrt{a^2-b})$
134619
Galois extension with $X^4-2aX^2+b\in\mathbb Q[X]$
6984
Inverting $a+b\sqrt{2}$ in the field $\Bbb Q(\sqrt{2})$
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
68389
Proving $ \frac{(a-b)^2}{8a}\leqslant\frac{a+b}{2} - \sqrt{ab} \leqslant\frac{(a-b)^2}{8b}$ when $ 0<b\le a$
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
32760
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
101164
Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
112368
Is there a rule for $\sqrt{a+b}$?
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
143831
Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
115282
Showing that $\mathbb Q(\sqrt{17})$ has class number 1
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$