Question

Find The Cube Root Of $46656$ By Prime Factorization Method

Answer 1

Finding the cube root of $46656$ by Prime Factorization.

Prime factor of $46656=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3$
$$\begin{gathered} =2^3\times 2^3\times 3^3\times 3^3 \\ ={(2\times 2\times 3\times 3)}^3 \\ ={\left(36\right)}^3 \end{gathered}$$
$$\begin{gathered} \Rightarrow \sqrt[3]{46656}=\sqrt[3]{{\left(36\right)}^3} \\ ={\left({36}^3\right)}^{\frac{1}{3}} \\ =36\left[\because {\left(a^n\right)}^m=a^{nm}\right] \end{gathered}$$

Hence, the cube root of $46656$ is $36$