Examine whether the following numbers are rational or irrational :

(i) $(3- \sqrt5)^2$

(ii) $(7 - \sqrt7)(7 + \sqrt7)$

(iii) $(2\sqrt3 + 3\sqrt2)^2$

(iv) $(2\sqrt3 - 3\sqrt2)(2\sqrt3 + 3\sqrt2)$

(v) $5\sqrt3 \times \sqrt{12}$

Write the least (smallest) rationalising factor of :

(i) $\sqrt{12}$

(ii) $2\sqrt{12}$

(iii) $\sqrt{18}$

(iv) $\dfrac{1}{\sqrt{5}}$

(v) $\sqrt\dfrac{2}{3}$

Rationalise the denominator and simplify :

$\dfrac{3}{4 - \sqrt3}$

Rationalise the denominator and simplify :

$\dfrac{2}{\sqrt5 + \sqrt3}$