Question

`( \sqrt[3]{n - 3} )( \sqrt[3]{n + 5} )`I don't follow how to multiply radical expressions.

Answer 1

To multiply the following radical, copy the common index and then multiply the radicands.

`(\sqrt[m]{x})(\sqrt[m]{y})=\sqrt[m]{xy}`

Thus, the given expression can be simplified as follows:

`(\sqrt[3]{n-3})(\sqrt[3]{n+5})=\sqrt[3]{(n-3)(n+5)}`

Simplify the expression under the radical sign.

`\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}`