Question
Answer
$$\sqrt{-2}\cdot\sqrt{-2}=-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{-2}\cdot\sqrt{-2}& \xlongequal{ }\sqrt{2}\cdot i\sqrt{2}\cdot i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{2}\cdot\sqrt{2}\cdot(-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\sqrt{2}\cdot\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ }-\sqrt{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2\end{aligned} $$ | |
| ① | $ i \cdot i = i^2 = -1 $ |
| ② | Put the minus sign in front of the result. |
| ③ | The square root of $ 4 $ is $ 2 $. |
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