Question
Answer
$$-3\sqrt{-162}=-27\sqrt{2}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3\sqrt{-162}& \xlongequal{ }-3\sqrt{162}i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-3\cdot \sqrt{ 81 \cdot 2 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-3\cdot \sqrt{ 81 } \cdot \sqrt{ 2 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-3\cdot9 \sqrt{ 2 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ }-27\sqrt{2}i\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 162. ( in this example we factored out $ 81 $ ) |
| ② | Rewrite $ \sqrt{ 81 \cdot 2 } $ as the product of two radicals. |
| ③ | The square root of $ 81 $ is $ 9 $. |
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