Prove that $\sqrt 2 + \sqrt 3$ is irrational
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
7966
How prove $ \sqrt{2}+\sqrt{3}>\pi$?
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
111094
Help with proving that $\pi$ is irrational
43985
Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
96204
Irrational number $\sqrt2$ proof
56802
Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
104548
Geometric proof for irrationality of $\pi$
153043
Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
92226
Prove $\sqrt6$ is irrational
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
31744
Proving that there is an irrational number between any two unequal rational numbers.
143733
Is this proof that $\sqrt 2$ is irrational correct?
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?