Fill in the blank to make the following statement true:
The square root of $121$ is ..........

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0 . \overline{001}$

Rationalise the denominator of the following expression and evaluate it by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$,and $\sqrt{5}=2.236$ up to three decimal places:
$\frac{\sqrt{2}}{2+\sqrt{2}}$

Simplify $: \frac{(25)^{\frac{3}{2}} \times (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times (8)^{\frac{4}{3}}}$

For each question,select the proper option from four options given,to make the statement true: $(5^{\frac{3}{4}})^{\frac{4}{3}} = \dots$

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