Irrational Numbers

Prove that $\sqrt{p}+\sqrt{q}$ is irrational, where $p,q$ are primes.

Prove that the given number is irrational.

$3+2\sqrt{5}$

Prove that the given number is irrational.

$\sqrt{5}$

Prove that the given number is irrational.

$6+\sqrt{2}$

Prove that the given number is irrational.

$\sqrt{3}+\sqrt{5}$

Prove that the given number is irrational.

$\frac{1}{\sqrt{2}}$