Simplify: $5 \sqrt{2} + 2 \sqrt{8} - 3 \sqrt{32} + 4 \sqrt{128}$ (in $\sqrt{2}$)

Simplify: $(3 \sqrt{5}-5 \sqrt{2})(4 \sqrt{5}+3 \sqrt{2})$

For each question,select the proper option from the four options given to make the statement true: $(\sqrt{5}+3)^{2}$ is a / an $\ldots \ldots \ldots$ number.

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

Fill in the blanks to make the following statement true: $\sqrt{2} \cdot \sqrt{3} \cdot \sqrt{6} = \dots$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.1\overline{34}$