Rationalise the denominator of the following: $\frac{\sqrt{40}}{\sqrt{3}}$

Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{\sqrt{10}-\sqrt{5}}{2}$

Simplify the following expression: $(\sqrt{15}+\sqrt{7})(\sqrt{15}-\sqrt{7})$

Rationalise the denominator in the following expression:
$\frac{1}{\sqrt{5}-\sqrt{3}}$

State whether the following statement is true:
There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.

Convert the following rational number into decimal form and state the kind of its decimal expansion:
$\frac{4}{13}$