Question
Answer
$$(2-\sqrt{5})\cdot(2-\sqrt{5})=9-4\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2-\sqrt{5})\cdot(2-\sqrt{5})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4-2\sqrt{5}-2\sqrt{5}+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9-4\sqrt{5}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 2- \sqrt{5}\right) } \cdot \left( 2- \sqrt{5}\right) = \color{blue}{2} \cdot2+\color{blue}{2} \cdot- \sqrt{5}\color{blue}{- \sqrt{5}} \cdot2\color{blue}{- \sqrt{5}} \cdot- \sqrt{5} = \\ = 4- 2 \sqrt{5}- 2 \sqrt{5} + 5 $$ |
| ② | Combine like terms |
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