To multiply the following radical, copy the common index and then multiply the radicands.
[tex](\sqrt[m]{x})(\sqrt[m]{y})=\sqrt[m]{xy}[/tex]
Thus, the given expression can be simplified as follows:
[tex](\sqrt[3]{n-3})(\sqrt[3]{n+5})=\sqrt[3]{(n-3)(n+5)}[/tex]
Simplify the expression under the radical sign.
[tex]\begin{gathered} (\sqrt[3]{n-3})(\sqrt[3]{n+5})=\sqrt[3]{n^2+5n-3n-15} \\ =\sqrt[3]{n^2+2n-15} \end{gathered}[/tex]
