The initial expression is
[tex]-4\sqrt[]{12}+\sqrt[]{75}[/tex]
This can be simplified as shown below
[tex]\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}[/tex]
Therefore,
[tex]\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}[/tex]
The answer is -3sqrt(3)
