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

In each of the following numbers rationalise the denominator

$\frac{30}{5 \sqrt{3}-3 \sqrt{5}}$

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

$0.404040 \ldots$

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

$(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})=\ldots \ldots \ldots$

Simplify the following:

$\frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}$

Convert following rational numbers in decimal form and state the kind of its decimal expansion

$\frac{25}{8}$