Fill in the blanks to make the following statement true: $\sqrt{7}$ is a/an $\ldots \ldots \ldots$ number.

$A$ rational number between $\sqrt{2}$ and $\sqrt{3}$ is

Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$

Represent $\sqrt{10}$ on the number line.

Represent $\sqrt{4.5}$ geometrically on the number line.

Recall,$\pi$ is defined as the ratio of the circumference (say $c$) of a circle to its diameter (say $d$). That is,$\pi = \frac{c}{d}$. This seems to contradict the fact that $\pi$ is irrational. How will you resolve this contradiction?