Answer
$$\sqrt{6}-\sqrt{54}+3\sqrt{12}+5\sqrt{3}=-2\sqrt{6}+11\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{6}-\sqrt{54}+3\sqrt{12}+5\sqrt{3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\sqrt{6}-3\sqrt{6}+6\sqrt{3}+5\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2\sqrt{6}+11\sqrt{3}\end{aligned} $$ | |
| ① | $$ - \sqrt{54} =
- \sqrt{ 3 ^2 \cdot 6 } =
- \sqrt{ 3 ^2 } \, \sqrt{ 6 } =
- 3 \sqrt{ 6 }$$ |
| ② | $$ 3 \sqrt{12} =
3 \sqrt{ 2 ^2 \cdot 3 } =
3 \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
3 \cdot 2 \sqrt{ 3 } =
6 \sqrt{ 3 } $$ |
| ③ | Combine like terms |
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