Prove that \( \sqrt{5} \) is irrational.
Prove that \( 3 + 2\sqrt{5} \) is irrational.
Prove that the following are irrationals:
(i) \( \dfrac{1}{\sqrt{2}} \)
(ii) \( 7\sqrt{5} \)
(iii) \( 6 + \sqrt{2} \).