Question
Answer
$$\sqrt{5}\cdot(\sqrt{8}-\sqrt{3})=2\sqrt{10}-\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{5}\cdot(\sqrt{8}-\sqrt{3})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{5}\cdot(2\sqrt{2}-\sqrt{3}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\sqrt{10}-\sqrt{15}\end{aligned} $$ | |
| ① | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ② | $$ \color{blue}{ \sqrt{5} } \cdot \left( 2 \sqrt{2}- \sqrt{3}\right) = \color{blue}{ \sqrt{5}} \cdot 2 \sqrt{2}+\color{blue}{ \sqrt{5}} \cdot- \sqrt{3} = \\ = 2 \sqrt{10}- \sqrt{15} $$ |
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