Question
Answer
$$\sqrt{2}\cdot(\sqrt{5}-6\sqrt{12})=\sqrt{10}-12\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{2}\cdot(\sqrt{5}-6\sqrt{12})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{2}\cdot(\sqrt{5}-12\sqrt{3}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\sqrt{10}-12\sqrt{6}\end{aligned} $$ | |
| ① | $$ - 6 \sqrt{12} =
-6 \sqrt{ 2 ^2 \cdot 3 } =
-6 \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
-6 \cdot 2 \sqrt{ 3 } =
-12 \sqrt{ 3 } $$ |
| ② | $$ \color{blue}{ \sqrt{2} } \cdot \left( \sqrt{5}- 12 \sqrt{3}\right) = \color{blue}{ \sqrt{2}} \cdot \sqrt{5}+\color{blue}{ \sqrt{2}} \cdot- 12 \sqrt{3} = \\ = \sqrt{10}- 12 \sqrt{6} $$ |
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