Find the cube root of $13824$by prime factorisation method.

The given cube root is $13824$

We obtain when we prime factorize,

$$\begin{gathered} 13824=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3 \\ \Rightarrow 2^3\times 2^3\times 2^3\times 3^3 \\ =\sqrt[3]{13824}=2\times 2\times 2\times 3 \\ \Rightarrow 24 \end{gathered}$$

Hence, option A is correct