Simplify $\left(4^{\frac{1}{5}}\right)^{3}$.

Rationalise the denominator of the following expression and evaluate it by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$,and $\sqrt{5}=2.236$ up to three decimal places:
$\frac{\sqrt{2}}{2+\sqrt{2}}$

Find the value of $a$ :
$\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a-6 \sqrt{3}$

Value of $\sqrt[4]{(81)^{-2}}$ is

If $\sqrt{2}=1.414$ and $\sqrt{3}=1.732,$ find the value of $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$

Find three different irrational numbers between the rational numbers $\frac{1}{4}$ and $\frac{4}{5}$.