Question
Answer
$$\sqrt{18}\cdot(2+\sqrt{6})-2\sqrt{3}=6\sqrt{2}+4\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{18}\cdot(2+\sqrt{6})-2\sqrt{3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3\sqrt{2}\cdot(2+\sqrt{6})-2\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6\sqrt{2}+6\sqrt{3}-2\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6\sqrt{2}+4\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{18} =
\sqrt{ 3 ^2 \cdot 2 } =
\sqrt{ 3 ^2 } \, \sqrt{ 2 } =
3 \sqrt{ 2 }$$ |
| ② | $$ \color{blue}{ 3 \sqrt{2} } \cdot \left( 2 + \sqrt{6}\right) = \color{blue}{ 3 \sqrt{2}} \cdot2+\color{blue}{ 3 \sqrt{2}} \cdot \sqrt{6} = \\ = 6 \sqrt{2} + 6 \sqrt{3} $$ |
| ③ | Combine like terms |
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