Answer
The standard form of $\sqrt{-75}-\sqrt{-12}$ is $3i\sqrt{3}$.
Work Step by Step
Consider the expression,
$\sqrt{-75}-\sqrt{-12}$
Rewrite $\sqrt{-75}-\sqrt{-12}$ as $\sqrt{75}\sqrt{-1}-\sqrt{12}\sqrt{-1}$
As $i=\sqrt{-1}$
Therefore,
$\begin{align}
& \sqrt{-75}-\sqrt{-12}=\sqrt{25\left( 3 \right)}i-\sqrt{4\left( 3 \right)}i \\
& =5\sqrt{3}i-2\sqrt{3}i
\end{align}$
Subtract the terms; combine the real part and imaginary part separately.
$\begin{align}
& 5\sqrt{3}i-2\sqrt{3}i=i\sqrt{3}\left( 5-2 \right) \\
& =i\sqrt{3}\left( 3 \right) \\
& =3i\sqrt{3}
\end{align}$
Thus,
$\sqrt{-75}-\sqrt{-12}=3i\sqrt{3}$
Hence, the standard form $\sqrt{-75}-\sqrt{-12}$ is $3i\sqrt{3}$.
