Answer
$$\sqrt{-90}=3\sqrt{10}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{-90}& \xlongequal{ }\sqrt{90}\cdot i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \sqrt{ 9 \cdot 10 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}} \sqrt{ 9 } \cdot \sqrt{ 10 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3\sqrt{10}i\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 90. ( in this example we factored out $ 9 $ ) |
| ② | Rewrite $ \sqrt{ 9 \cdot 10 } $ as the product of two radicals. |
| ③ | The square root of $ 9 $ is $ 3 $. |
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Simplify Radical Expression