Simplify the following:

$\sqrt{45}-3 \sqrt{20}+4 \sqrt{5}$

State whether the following statements are true or false? Justify your answer.

$\frac{\sqrt{15}}{\sqrt{3}}$ is written in the form $\frac{p}{q},$ where $q \neq 0$ so it is a rational number.

State whether each of the following statements is true or false

Each integer is a whole number.

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

$\left(5^{-2}\right)^{3}=\ldots \ldots \ldots$

Which of the following is irrational?

Find the value of $a$ :

$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$