Find the side of a cube whose volume is $

Volume of a cube with side s is given by: 

$V=s^{3}$

$\therefore s=\sqrt[3]{\bar{V}}$

$=\sqrt[3]{\frac{24389}{216}}$

$=\frac{\sqrt[3]{24389}}{\sqrt[3]{216}}$

$=\frac{\sqrt[3]{29 \times 29 \times 29}}{\sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3}}$   (By prime factorisation)

$=\frac{29}{2 \times 3}$

$=\frac{29}{6}$

Thus, the length of the side is $\frac{29}{6} \mathrm{~m}$.