Question
Answer
$$\sqrt{6}\cdot(7\sqrt{12}-4\sqrt{3})=30\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{6}\cdot(7\sqrt{12}-4\sqrt{3})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{6}\cdot(14\sqrt{3}-4\sqrt{3}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\sqrt{6}\cdot10\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}30\sqrt{2}\end{aligned} $$ | |
| ① | $$ 7 \sqrt{12} =
7 \sqrt{ 2 ^2 \cdot 3 } =
7 \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
7 \cdot 2 \sqrt{ 3 } =
14 \sqrt{ 3 } $$ |
| ② | Combine like terms |
| ③ | $$ 10 \sqrt{18} =
10 \sqrt{ 3 ^2 \cdot 2 } =
10 \sqrt{ 3 ^2 } \, \sqrt{ 2 } =
10 \cdot 3 \sqrt{ 2 } =
30 \sqrt{ 2 } $$ |
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