Answer
$$\sqrt{81}-\sqrt{-147}+\sqrt{1}+\sqrt{-108}=9-\sqrt{-147}+1+6\sqrt{3}i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{81}-\sqrt{-147}+\sqrt{1}+\sqrt{-108}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9-\sqrt{-147}+1+\sqrt{-108} \xlongequal{ } \\[1 em] & \xlongequal{ }9-\sqrt{-147}+1+\sqrt{108}\cdot i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9-\sqrt{-147}+1 + \sqrt{ 36 \cdot 3 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9-\sqrt{-147}+1 + \sqrt{ 36 } \cdot \sqrt{ 3 } i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9-\sqrt{-147}+1+6\sqrt{3}i\end{aligned} $$ | |
| ① | $$ \sqrt{81} = 9 $$ |
| ② | Factor out the largest perfect square of 108. ( in this example we factored out $ 36 $ ) |
| ③ | Rewrite $ \sqrt{ 36 \cdot 3 } $ as the product of two radicals. |
| ④ | The square root of $ 36 $ is $ 6 $. |
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