[tex]\sqrt[3]{5} \cdot \sqrt{2} = \frac{\sqrt[3]{5 \cdot 2}}{\sqrt[3]{2}} \cdot \sqrt{2}[/tex]
[tex]= \sqrt[3]{10} \cdot \sqrt[6]{2}[/tex]
[tex]= \sqrt[3]{10} \cdot \frac{\sqrt[6]{200}}{\sqrt[6]{100}}[/tex]
[tex]= \sqrt[3]{10} \cdot \frac{\sqrt[6]{200}}{\sqrt[6]{10^{2}}}[/tex]
[tex]= \sqrt[6]{200}[/tex]
(ie B)
I may have performed unnecessary steps, but that's my process.
