Question
Answer
$$(\sqrt{5}-5\sqrt{2})(\sqrt{5}+\sqrt{2})=-5-4\sqrt{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\sqrt{5}-5\sqrt{2})(\sqrt{5}+\sqrt{2})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5+\sqrt{10}-5\sqrt{10}-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-5-4\sqrt{10}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( \sqrt{5}- 5 \sqrt{2}\right) } \cdot \left( \sqrt{5} + \sqrt{2}\right) = \color{blue}{ \sqrt{5}} \cdot \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot \sqrt{2}\color{blue}{- 5 \sqrt{2}} \cdot \sqrt{5}\color{blue}{- 5 \sqrt{2}} \cdot \sqrt{2} = \\ = 5 + \sqrt{10}- 5 \sqrt{10}-10 $$ |
| ② | Combine like terms |
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