Question
Answer
$$-\sqrt{81}+\sqrt{-18}+\sqrt{121}+\sqrt{-8}=-9+\sqrt{-18}+11+2\sqrt{2}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\sqrt{81}+\sqrt{-18}+\sqrt{121}+\sqrt{-8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-9+\sqrt{-18}+11+\sqrt{-8} \xlongequal{ } \\[1 em] & \xlongequal{ }-9+\sqrt{-18}+11+\sqrt{8}\cdot i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-9+\sqrt{-18}+11 + \sqrt{ 4 \cdot 2 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-9+\sqrt{-18}+11 + \sqrt{ 4 } \cdot \sqrt{ 2 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-9+\sqrt{-18}+11+2\sqrt{2}i\end{aligned} $$ | |
| ① | $$ - \sqrt{81} = -1 \cdot 9 = -9 $$ |
| ② | $$ \sqrt{121} = 11 $$ |
| ③ | Factor out the largest perfect square of 8. ( in this example we factored out $ 4 $ ) |
| ④ | Rewrite $ \sqrt{ 4 \cdot 2 } $ as the product of two radicals. |
| ⑤ | The square root of $ 4 $ is $ 2 $. |
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