Question
Answer
$$3\sqrt{-24}\cdot2\sqrt{-18}=6\sqrt{6}i\cdot23\sqrt{2}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\sqrt{-24}\cdot2\sqrt{-18}& \xlongequal{ }3\sqrt{24}i\cdot2\sqrt{18}\cdot i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot \sqrt{ 4 \cdot 6 } \, i \cdot 2 \cdot \sqrt{ 9 \cdot 2 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3\cdot \sqrt{ 4 } \cdot \sqrt{ 6 } \, i \cdot 2 \cdot \sqrt{ 9 } \cdot \sqrt{ 2 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}3\cdot2 \sqrt{ 6 } \, i \cdot 2 \cdot 3\sqrt{2}i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}6\sqrt{6}i\cdot23\sqrt{2}i\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 24. ( in this example we factored out $ 4 $ ) |
| ② | Factor out the largest perfect square of 18. ( in this example we factored out $ 9 $ ) |
| ③ | Rewrite $ \sqrt{ 4 \cdot 6 } $ as the product of two radicals. |
| ④ | Rewrite $ \sqrt{ 9 \cdot 2 } $ as the product of two radicals. |
| ⑤ | The square root of $ 4 $ is $ 2 $. |
| ⑥ | The square root of $ 9 $ is $ 3 $. |
| ⑦ | The square root of $ 9 $ is $ 3 $. |
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Simplify Radical Expression