$\sqrt{m}+\sqrt{n}\notin\mathbb{Q}$ Irrationals, Roots Proof
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
20315
$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
109953
How to prove that $\sqrt 3$ is an irrational number?
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
50930
Proving the continued fraction representation of $\sqrt{2}$
8087
Algebraic integers of $\mathbb{Q}(\sqrt{m})$ for $m$ a squarefree integer
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
30622
Proving $\sqrt 3$ is irrational.
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
143733
Is this proof that $\sqrt 2$ is irrational correct?
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
53945
The square root of a prime number is irrational