for two primes p and q, $\sqrt{p}$ +$\sqrt{q}$ is irrational?
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
122226
Incorrect logic in popular proof of the irrationality of $\sqrt2$?
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
130499
How can $p^{q+1}+q^{p+1}$ be a perfect square?
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
86988
Cardinality of the Irrationals
132115
Verify my proof of the irrationality of $\sqrt{6}$.
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
11069
Deciding whether $2^{\sqrt2}$ is irrational/transcendental
45454
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
2926
The contradiction method used to prove that the square root of a prime is irrational
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
6275
How can you prove that the square root of two is irrational?
67605
Different proof that $\sqrt{2}$ is irrational
158066
Prove $2^{1/3}$ is irrational.
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?