Rationalise the denominator of the following:
$\frac{2+\sqrt{3}}{2-\sqrt{3}}$

Rationalise the denominator in each of the following:
$\frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}$

Fill in the blanks to make the following statement true: $\sqrt{2} \cdot \sqrt{3} \cdot \sqrt{6} = \dots$

Simplify each of the following expressions:
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$

Simplify the following expression: $(3+\sqrt{5})(4-\sqrt{11})$

For each question,select the proper option from four options given,to make the statement true: The rationalising factor of $4-\sqrt{5}$ is...........