Question

Find the cube roots of the following numbers.
(1) 5832
(2) 4096

Answer 1

(1)

$$\begin{gathered} \because 5832=2^3\times 3^6=2^3\times {\left(3^2\right)}^3={\left(2\times 3^2\right)}^3={\left(18\right)}^3 \\ \therefore \sqrt[3]{5832}=18 \end{gathered}$$

(2)

$$\begin{gathered} \because 4096=2^{12}={\left(2^4\right)}^3={\left(16\right)}^3 \\ \therefore \sqrt[3]{4096}=16 \end{gathered}$$