Add $: 0 . \overline{3}+0.4 \overline{7}$

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$\sqrt{5} \times \sqrt{5}$ is a / an $\ldots \ldots \ldots$ number.

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

$(i)$ The square of an irrational number is always rational.

$(ii)$ $\frac{\sqrt{12}}{\sqrt{3}}$ is not a rational number as $\sqrt{12}$ and $\sqrt{3}$ are not integers.

Locate $\sqrt{13}$ on the number line.

Simplify the following:

$\frac{2 \sqrt{3}}{3}-\frac{\sqrt{3}}{6}$

Represent the following numbers on the number line:

$7,7.2, \frac{-3}{2}, \frac{-12}{5}$