Question

Which radical expression represents the following after being multiplied and simplified completely?

Answer 1

Step-by-step explanation:

Given:

`\sqrt[]{5}(4+\sqrt[]{8})`

To find the equivalent value, we simplify the given expression first. So,

`\begin{gathered} \sqrt[]{5}(4+\sqrt[]{8}) \\ =(\sqrt[]{5)}(4)+(\sqrt[]{5})(\sqrt[]{8)} \\ Simplify\text{ } \\ =(\sqrt[]{5)}(4)+(\sqrt[]{5})(2\sqrt[]{2}) \end{gathered}`

We apply the radical rule:

So,

Hence,

`\begin{gathered} =(\sqrt[]{5)}(4)+(\sqrt[]{5})(2\sqrt[]{2}) \\ =4\sqrt[]{5}+2\sqrt[]{10} \end{gathered}`

Therefore, the answer is: