Question
Answer
$$5\sqrt{3}-\sqrt{72}+\sqrt{243}+\sqrt{8}=14\sqrt{3}-4\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{3}-\sqrt{72}+\sqrt{243}+\sqrt{8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5\sqrt{3}-6\sqrt{2}+9\sqrt{3}+2\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}14\sqrt{3}-4\sqrt{2}\end{aligned} $$ | |
| ① | $$ - \sqrt{72} =
- \sqrt{ 6 ^2 \cdot 2 } =
- \sqrt{ 6 ^2 } \, \sqrt{ 2 } =
- 6 \sqrt{ 2 }$$ |
| ② | $$ \sqrt{243} =
\sqrt{ 9 ^2 \cdot 3 } =
\sqrt{ 9 ^2 } \, \sqrt{ 3 } =
9 \sqrt{ 3 }$$ |
| ③ | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ④ | Combine like terms |
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