Proving irrationality of $\sqrt[3]{3}+\sqrt[3]{9}$
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
139117
Proving $\lim_{x\to9}\sqrt x=3$ using Cauchy's definition
30478
How to prove that a number is irrational
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
60073
Proving $4(a^3 + b^3) \ge (a + b)^3$ and $9(a^3 + b^3 + c^3) \ge (a + b + c)^3$
91101
Proving $\sqrt2$ 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?
86988
Cardinality of the Irrationals
55077
prove that $2\sqrt5 +\sqrt{11}$ is irrational
75204
Irrationality $\sqrt{2}$ with ideal
143733
Is this proof that $\sqrt 2$ is irrational correct?