Find the value

$\frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$

Simplify the following:

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

Convert following rational numbers in decimal form and state the kind of its decimal expansion

$\frac{4}{13}$

Represent $\sqrt{7.5}$ on the number line.

State whether the following statements are true or false? Justify your answer.

$(i)$ Number of rational numbers between $15$ and $18$ is finite.

$(ii)$ There are numbers which cannot be written in the form $\frac{p}{q}, q \neq 0, p , q$ both are integers.

Find the values of $a$ and $b$ in each of the following:

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11} \sqrt{5} b$