Prove $\sqrt{2} + \sqrt{5}$ is irrational
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
2926
The contradiction method used to prove that the square root of a prime is irrational
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
114793
Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
126199
Proof of $\pi$ not being a quadratic irrational number.
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
116277
real values of $x$ in $\sqrt{5-x} = 5-x^2$.
99311
Prove $2^{1/3} + 2^{2/3}$ is irrational
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
43985
Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
56802
Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
31744
Proving that there is an irrational number between any two unequal rational numbers.