Answer
The standard form of the expression $\sqrt{-32}-\sqrt{-18}$ is $i\sqrt{2}$.
Work Step by Step
Consider the expression,
$\sqrt{-32}-\sqrt{-18}$
Rewrite the expression $\sqrt{-32}-\sqrt{-18}$ as $\sqrt{32}\sqrt{-1}-\sqrt{18}\sqrt{-1}$
As $\sqrt{-1}=i$
$\begin{align}
& \sqrt{32}\sqrt{-1}-\sqrt{18}\sqrt{-1}=i\sqrt{16\left( 2 \right)}-i\sqrt{9\left( 2 \right)} \\
& =4i\sqrt{2}-3i\sqrt{2}
\end{align}$
To subtract two complex numbers, combine the real numbers together and the terms containing $i$.
$\begin{align}
& 4i\sqrt{2}-3i\sqrt{2}=i\sqrt{2}\left( 4-3 \right) \\
& =i\sqrt{2}\left( 1 \right) \\
& =i\sqrt{2}
\end{align}$
Hence, the standard form of the expression $\sqrt{-32}-\sqrt{-18}$ is $i\sqrt{2}$.
