Question

Write in ascending order: $2\sqrt[3]{5}\mathrm{and}3\sqrt[3]{2}$.

Answer 1

Solutions:

The given roots of the numbers $2\sqrt[3]{5}\mathrm{and}3\sqrt[3]{2}$ can be written as,

$$\begin{gathered} 2\sqrt[3]{5}=\sqrt[3]{2\times 2\times 2\times 5}=\sqrt[3]{40} \\ 3\sqrt[3]{2}=\sqrt[3]{3\times 3\times 3\times 2}=\sqrt[3]{54} \\ \because 40<54 \\ \therefore 2\sqrt[3]{5}<3\sqrt[3]{2} \end{gathered}$$

Hence, $\mathbf{2}\sqrt[\mathbf{3}]{\mathbf{5}}\mathbf{<}\mathbf{3}\sqrt[\mathbf{3}]{\mathbf{2}}$