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 $\sqrt{5}=2.236$

$\frac{\sqrt{10}-\sqrt{5}}{2}$

Simplify

$3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}$

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

$0 . \overline{35}$

Find the value of $b$ :

$\frac{\sqrt{2}+\sqrt{3}}{3 \sqrt{2}-2 \sqrt{3}}=2-b \sqrt{6}$

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

The rationalising factor of $4-\sqrt{5}$ is...........

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

$0.5 \overline{7}$