Question

what is the value of cube root 0f 144 * cube root of 1500

Answer 1

$$\begin{gathered} \sqrt[3]{144}\times \sqrt[3]{1500} \\ =\sqrt[3]{2\times 2\times 3\times 2\times 2\times 3}\times \sqrt[3]{3\times 5\times 5\times 5\times 2\times 2} \\ =\sqrt[3]{2\times 2\times 3\times 2\times 2\times 3}\times \sqrt[3]{3\times 5\times 5\times 5\times 2\times 2} \\ =\sqrt[3]{2\times 2\times 3\times 2\times 2\times 3\times 3\times 5\times 5\times 5\times 2\times 2} \\ \mathrm{re}-\mathrm{arranging}\mathrm{we}\mathrm{get} \\ =\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5} \\ \mathrm{grouping}\mathrm{them}\mathrm{in}\mathrm{three}\mathrm{and}\mathrm{bringing}\mathrm{them}\mathrm{out}\mathrm{of}\mathrm{cube}\mathrm{root},\mathrm{we}\mathrm{get} \\ =2\times 2\times 3\times 5 \\ =60\left(\mathrm{answer}\right) \end{gathered}$$