Question
Answer
$$2\sqrt{6}+4\sqrt{3}+\sqrt{27}+\sqrt{54}=5\sqrt{6}+7\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\sqrt{6}+4\sqrt{3}+\sqrt{27}+\sqrt{54}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\sqrt{6}+4\sqrt{3}+3\sqrt{3}+3\sqrt{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5\sqrt{6}+7\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{27} =
\sqrt{ 3 ^2 \cdot 3 } =
\sqrt{ 3 ^2 } \, \sqrt{ 3 } =
3 \sqrt{ 3 }$$ |
| ② | $$ \sqrt{54} =
\sqrt{ 3 ^2 \cdot 6 } =
\sqrt{ 3 ^2 } \, \sqrt{ 6 } =
3 \sqrt{ 6 }$$ |
| ③ | Combine like terms |
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