Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.2555 \ldots$

Let $x$ be a rational number and $y$ be an irrational number. Is $xy$ necessarily irrational? Justify your answer with an example.

State whether the following statement is true or false:
$(-5)^{2} = -25$

State whether the following statements are true or false. Justify your answer.
$(i)$ The number of rational numbers between $15$ and $18$ is finite.
$(ii)$ There are numbers which cannot be written in the form $\frac{p}{q}$,where $q \neq 0$ and $p, q$ are both integers.

Simplify the following:
$\frac{2 \sqrt{3}}{3} - \frac{\sqrt{3}}{6}$

Which of the following is irrational?