Let $x$ be rational and $y$ be irrational. Is xy necessarily irrational? Justify your answer by an example.
Simplify : $(3 \sqrt{5}-5 \sqrt{2})(4 \sqrt{5}+3 \sqrt{2})$
Find the value of $a$ :
$\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$
Visualise the representation of $2.6 \overline{4}$ on the number line up to $5$ decimal places, that is up to $2.64444$
Simplify
$\left(4^{\frac{1}{5}}\right)^{3}$