Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$

$\frac{\sqrt{2}}{2+\sqrt{2}}$

Find the values of $a$ and $b$ in each of the following:

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11} \sqrt{5} b$

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

$\frac{6}{\sqrt{6}}$

Represent geometrically numbers on the number line:

$\sqrt{8.1}$

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$(\sqrt{5}+3)^{2}$ is a $/$ an $\ldots \ldots \ldots$ number.

Express $0.12 \overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$