Prove that $\sqrt[3]{2}+\sqrt[3]{4}$ is irrational
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
113359
Proving that $x^2 + 4$ is not divisible by $3$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
51518
Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
96204
Irrational number $\sqrt2$ proof
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
32
Is $n^{th}$ root of $2$ an irrational number?
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
53945
The square root of a prime number is irrational
104548
Geometric proof for irrationality of $\pi$
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
153043
Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
101162
Square root of $2$ is irrational