Prove that $\sqrt[3]5 - \sqrt[4]3$ is Irrational
20315
$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
67605
Different proof that $\sqrt{2}$ is irrational
15110
About irrational logarithms
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
115834
Cubic polynomial with three (distinct) irrational roots
153043
Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
129433
$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational
56464
Proving the irrationality of $e^n$
17930
Please explain this step in proving the square root of 3 is irrational
18360
Proof that the irrational numbers are uncountable
116054
The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
2926
The contradiction method used to prove that the square root of a prime is irrational
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
126199
Proof of $\pi$ not being a quadratic irrational number.
146015
Computing $\int \sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{x\cdots}}}} \,\mathrm{d}x$
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
110282
Use the unique factorization for integers theorem and the definition of logarithm to prove that $\log_3 (7)$ is irrational.