Given the numbers:
[tex]8\sqrt[]{5},5\sqrt[]{10}[/tex]The product of the numbers will be:
[tex]\begin{gathered} 8\sqrt[]{5}\times5\sqrt[]{10}=8\times5\sqrt[]{5\times10}=40\sqrt[]{50} \\ \\ 50=25\times2=5^2\times2 \\ \\ 40\sqrt[]{50}=40\sqrt[]{5^2\times2}=40\times5\sqrt[]{2}=200\sqrt[]{2} \end{gathered}[/tex]So, the answer will be:
[tex]200\sqrt[]{2}[/tex]