Answer
$$\sqrt{-108}=6\sqrt{3}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{-108}& \xlongequal{ }\sqrt{108}\cdot i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \sqrt{ 36 \cdot 3 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}} \sqrt{ 36 } \cdot \sqrt{ 3 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6\sqrt{3}i\end{aligned} $$ | |
| 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 $. |
This page was created using
Simplify Radical Expression