Question
Answer
$$\sqrt{2}\cdot\dfrac{2+\sqrt{2}}{2}=\sqrt{2}+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{2}\cdot\frac{2+\sqrt{2}}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{2}+2}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{2}+1}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\sqrt{2}+1\end{aligned} $$ | |
| ① | $$ \color{blue}{ \sqrt{2} } \cdot \left( 2 + \sqrt{2}\right) = \color{blue}{ \sqrt{2}} \cdot2+\color{blue}{ \sqrt{2}} \cdot \sqrt{2} = \\ = 2 \sqrt{2} + 2 $$$$ \color{blue}{ 1 } \cdot 2 = 2 $$ |
| ② | Divide both numerator and denominator by 2. |
| ③ | Remove 1 from denominator. |
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