The number obtained on rationalizing the denominator of $\frac{1}{7-\sqrt{2}}$ is

For each question,select the proper option from four options given,to make the statement true: $.............$ is a rational number between $7$ and $8$.

Find the value of the following expression correct to three decimal places,taking $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$:
$\frac{\sqrt{10} - \sqrt{5}}{2}$

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.
$\frac{1}{\sqrt{3}+\sqrt{2}}$

If $a = 2 + \sqrt{3}$,then find the value of $a - \frac{1}{a}$.

Represent the following numbers on the number line:
$7, 7.2, \frac{-3}{2}, \frac{-12}{5}$