Simplify the following:
$\sqrt{45}-3 \sqrt{20}+4 \sqrt{5}$

Find three rational numbers between $\frac{1}{4}$ and $\frac{1}{5}$.

For each question,select the proper option from four options given,to make the statement true: $\sqrt{5^{2}+12^{2}}$ is a / an $\ldots \ldots$ 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.

Find three different irrational numbers lying between $\sqrt{3}$ and $\sqrt{5}$.

Rationalise the denominator of the following expression:
$\frac{4}{\sqrt{10}+\sqrt{6}}$