First we write the expression
[tex]\begin{gathered} -\sqrt[]{-75} \\ \text{Simplifying, we have} \\ -\sqrt[]{-75}=-\sqrt[]{-1\times3\times25} \end{gathered}[/tex]
Therefore,
[tex]-\sqrt[]{-75}=-\sqrt[]{-1}\times\sqrt[]{3}\text{ }\times\sqrt[]{25}[/tex]
Hence,
[tex]-\sqrt[]{-75}=-\sqrt[]{-1}\times\sqrt[]{3}\text{ }\times5[/tex]
In mathematics, there is a symbol, i, used to define complex numbers.
i is as defined below
[tex]i=\sqrt[]{-1}[/tex]
Therefore,
[tex]\begin{gathered} -\sqrt[]{-75}=-i\times\sqrt[]{3}\text{ }\times5 \\ -\sqrt[]{-75}=-5i\sqrt[]{3} \end{gathered}[/tex]
Hence, the expression simplified is
-5i√3
D
