Rationalise the denominator in each of the following

$\frac{1}{7-4 \sqrt{3}}$

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

If $(\sqrt{5}+3)^{2}=a+b \sqrt{5},$ then........

Express $0 . \overline{83}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$.

Insert a rational number and an irrational number between the following:

$0$ and $0.1$

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 $\sqrt{5}=2.236$

$\frac{4}{3 \sqrt{3}-2 \sqrt{2}}+\frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

$\sqrt[4]{\sqrt[3]{2^{2}}}$ equals