Answer
$$3\sqrt{-108}=18\sqrt{3}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\sqrt{-108}& \xlongequal{ }3\sqrt{108}i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3\cdot \sqrt{ 36 \cdot 3 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot \sqrt{ 36 } \cdot \sqrt{ 3 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3\cdot6 \sqrt{ 3 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ }18\sqrt{3}i\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 108. ( in this example we factored out $ 36 $ ) |
| ② | Rewrite $ \sqrt{ 36 \cdot 3 } $ as the product of two radicals. |
| ③ | The square root of $ 36 $ is $ 6 $. |
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