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