If $k_1, \ldots, k_n$ are non-square, pairwise coprime, then $\sqrt {k_n} \not \in \mathbf{Q}(\sqrt {k_1}, \ldots, \sqrt {k_{n-1}})$
6869
The square roots of different primes are linearly independent over the field of rationals
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
51518
Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
8087
Algebraic integers of $\mathbb{Q}(\sqrt{m})$ for $m$ a squarefree integer
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
71935
Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?