Question
Answer
$$\sqrt{3}\cdot(5\sqrt{3}-\sqrt{12}+\sqrt{10})=9+\sqrt{30}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{3}\cdot(5\sqrt{3}-\sqrt{12}+\sqrt{10})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{3}\cdot(5\sqrt{3}-2\sqrt{3}+\sqrt{10}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\sqrt{3}\cdot(3\sqrt{3}+\sqrt{10}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9+\sqrt{30}\end{aligned} $$ | |
| ① | $$ - \sqrt{12} =
- \sqrt{ 2 ^2 \cdot 3 } =
- \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
- 2 \sqrt{ 3 }$$ |
| ② | Combine like terms |
| ③ | $$ \color{blue}{ \sqrt{3} } \cdot \left( 3 \sqrt{3} + \sqrt{10}\right) = \color{blue}{ \sqrt{3}} \cdot 3 \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot \sqrt{10} = \\ = 9 + \sqrt{30} $$ |
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