Rationalise the denominator in each of the following and hence evaluate by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$ and $\sqrt{5}=2.236,$ up to three decimal places.
$\frac{\sqrt{10}-\sqrt{5}}{2}$

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.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$
$0.\overline{125}$

If $\sqrt{2} = 1.4142$,then evaluate $\sqrt{5} \div \sqrt{10}$ correct to four decimal places.

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

Insert a rational number and an irrational number between the following:
$6.375289$ and $6.375738$