Simplify: $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$
In each of the following numbers rationalise the denominator
$\frac{30}{5 \sqrt{3}-3 \sqrt{5}}$
In each of the following numbers rationalise the denominator
$\frac{n^{2}}{\sqrt{m^{2}+n^{2}}+m}$
Rationalise the denominator in each of the following
$\frac{1}{\sqrt{5}-\sqrt{3}}$
Find the value
$\frac{8 \frac{1}{3} \times 16 \frac{1}{3}}{32^{-\frac{1}{3}}}$