Question
Answer
$$\sqrt{5}\cdot(\sqrt{12}+\sqrt{2})=2\sqrt{15}+\sqrt{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{5}\cdot(\sqrt{12}+\sqrt{2})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{5}\cdot(2\sqrt{3}+\sqrt{2}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\sqrt{15}+\sqrt{10}\end{aligned} $$ | |
| ① | $$ \sqrt{12} =
\sqrt{ 2 ^2 \cdot 3 } =
\sqrt{ 2 ^2 } \, \sqrt{ 3 } =
2 \sqrt{ 3 }$$ |
| ② | $$ \color{blue}{ \sqrt{5} } \cdot \left( 2 \sqrt{3} + \sqrt{2}\right) = \color{blue}{ \sqrt{5}} \cdot 2 \sqrt{3}+\color{blue}{ \sqrt{5}} \cdot \sqrt{2} = \\ = 2 \sqrt{15} + \sqrt{10} $$ |
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