Question

What is −412−−√+75−−√ in simplest radical form? Enter your answer in the box.

Answer 1

The initial expression is

`-4\sqrt[]{12}+\sqrt[]{75}`

This can be simplified as shown below

`\begin{gathered} -4\sqrt[]{12}+\sqrt[]{75}=-4\sqrt[]{3\cdot4}+\sqrt[]{25\cdot3} \\ =-4\sqrt[]{4}\cdot\sqrt[]{3}+\sqrt[]{25}\cdot\sqrt[]{3} \\ \end{gathered}`

Therefore,

`\begin{gathered} \Rightarrow-4\sqrt[]{12}+\sqrt[]{75}=-4\cdot2\sqrt[]{3}+5\sqrt[]{3} \\ =-8\sqrt[]{3}+5\sqrt[]{3} \\ =-3\sqrt[]{3} \\ \Rightarrow-4\sqrt[]{12}+\sqrt[]{75}=-3\sqrt[]{3} \end{gathered}`

The answer is -3sqrt(3)