Question

Find the cube root of $13824$ number by Prime Factorization Method.

Answer 1

Finding the cube root of $13824$ by Prime Factorization.

Prime factor of $13824=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$
$$\begin{gathered} =2^3\times 2^3\times 2^3\times 3^3 \\ ={(2\times 2\times 2\times 3)}^3={\left(24\right)}^3 \end{gathered}$$
$$\begin{gathered} \Rightarrow \sqrt[3]{13824}=\sqrt[3]{{\left(24\right)}^3} \\ ={\left({24}^3\right)}^{\frac{1}{3}} \\ =24\left[\because {\left(a^n\right)}^m=a^{nm}\right] \end{gathered}$$

Hence, the cube root of $13824$ is $24$.