Find conditions on positive integers so that $\sqrt{a}+\sqrt{b}+\sqrt{c}$ is irrational
62058
How to prove $1$,$\sqrt{2},\sqrt{3}$ and $\sqrt{6}$ are linearly independent over $\mathbb{Q}$?
67031
use contradiction to prove that the square root of $p$ is irrational
32848
Prove that the product of a non-zero rational and irrational number is irrational.
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
114793
Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
104548
Geometric proof for irrationality of $\pi$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
48035
Prove that square root of 2 is irrational using the principle of Mathematical Induction
89716
Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
40009
Show that $e^{\sqrt 2}$ is irrational
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
19076
If a.b.c,d are rationals and x is irrational number, then prove that $\frac{ax+b}{cx+d}$ is usually a irrational number. When do exceptions occur?
158066
Prove $2^{1/3}$ is irrational.
109953
How to prove that $\sqrt 3$ is an irrational number?