Question
Answer
$$(2+\sqrt{2})\cdot(-1+\sqrt{2})=\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2+\sqrt{2})\cdot(-1+\sqrt{2})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-2+2\sqrt{2}-\sqrt{2}+2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\sqrt{2}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 2 + \sqrt{2}\right) } \cdot \left( -1 + \sqrt{2}\right) = \color{blue}{2} \cdot-1+\color{blue}{2} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot-1+\color{blue}{ \sqrt{2}} \cdot \sqrt{2} = \\ = -2 + 2 \sqrt{2}- \sqrt{2} + 2 $$ |
| ② | Combine like terms |
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