Question
Answer
$$5\sqrt{-8}+3\sqrt{-18}=10\sqrt{2}i+9\sqrt{2}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{-8}+3\sqrt{-18}& \xlongequal{ }5\sqrt{8}i+3\sqrt{18}i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5\cdot \sqrt{ 4 \cdot 2 } \, i + 3\cdot \sqrt{ 9 \cdot 2 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5\cdot \sqrt{ 4 } \cdot \sqrt{ 2 } \, i + 3\cdot \sqrt{ 9 } \cdot \sqrt{ 2 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}5\cdot2 \sqrt{ 2 } \, i + 3\cdot3 \sqrt{ 2 } \, i \xlongequal{ } \\[1 em] & \xlongequal{ }10\sqrt{2}i+9\sqrt{2}i\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 8. ( 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 2 } $ 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 $. |
This page was created using
Simplify Radical Expression