Question
Answer
$$4\sqrt{54}-\sqrt{24}+3\sqrt{80}-7\sqrt{20}=10\sqrt{6}-2\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4\sqrt{54}-\sqrt{24}+3\sqrt{80}-7\sqrt{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}12\sqrt{6}-2\sqrt{6}+12\sqrt{5}-14\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}10\sqrt{6}-2\sqrt{5}\end{aligned} $$ | |
| ① | $$ 4 \sqrt{54} =
4 \sqrt{ 3 ^2 \cdot 6 } =
4 \sqrt{ 3 ^2 } \, \sqrt{ 6 } =
4 \cdot 3 \sqrt{ 6 } =
12 \sqrt{ 6 } $$ |
| ② | $$ - \sqrt{24} =
- \sqrt{ 2 ^2 \cdot 6 } =
- \sqrt{ 2 ^2 } \, \sqrt{ 6 } =
- 2 \sqrt{ 6 }$$ |
| ③ | $$ 3 \sqrt{80} =
3 \sqrt{ 4 ^2 \cdot 5 } =
3 \sqrt{ 4 ^2 } \, \sqrt{ 5 } =
3 \cdot 4 \sqrt{ 5 } =
12 \sqrt{ 5 } $$ |
| ④ | $$ - 7 \sqrt{20} =
-7 \sqrt{ 2 ^2 \cdot 5 } =
-7 \sqrt{ 2 ^2 } \, \sqrt{ 5 } =
-7 \cdot 2 \sqrt{ 5 } =
-14 \sqrt{ 5 } $$ |
| ⑤ | Combine like terms |
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