Show that each of the following is irrational :

(i) $\Big(2 + \sqrt{5}\Big)^2$

(ii) $\Big(3 - \sqrt{3}\Big)^2$

(iii) $\Big(\sqrt{5} + \sqrt{3}\Big)^2$

(iv) $\dfrac{6}{\sqrt{3}}$

Prove that $\sqrt{5}$ is irrational number.

Prove that $\Big(\sqrt{3} + \sqrt{7}\Big)$ is irrational.

Prove that $(\sqrt{2} + \sqrt{3})$ is irrational.