Question
Answer
$$5\sqrt{18}-\sqrt{32}+5\sqrt{72}-\sqrt{45}=41\sqrt{2}-3\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{18}-\sqrt{32}+5\sqrt{72}-\sqrt{45}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}15\sqrt{2}-4\sqrt{2}+30\sqrt{2}-3\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}41\sqrt{2}-3\sqrt{5}\end{aligned} $$ | |
| ① | $$ 5 \sqrt{18} =
5 \sqrt{ 3 ^2 \cdot 2 } =
5 \sqrt{ 3 ^2 } \, \sqrt{ 2 } =
5 \cdot 3 \sqrt{ 2 } =
15 \sqrt{ 2 } $$ |
| ② | $$ - \sqrt{32} =
- \sqrt{ 4 ^2 \cdot 2 } =
- \sqrt{ 4 ^2 } \, \sqrt{ 2 } =
- 4 \sqrt{ 2 }$$ |
| ③ | $$ 5 \sqrt{72} =
5 \sqrt{ 6 ^2 \cdot 2 } =
5 \sqrt{ 6 ^2 } \, \sqrt{ 2 } =
5 \cdot 6 \sqrt{ 2 } =
30 \sqrt{ 2 } $$ |
| ④ | $$ - \sqrt{45} =
- \sqrt{ 3 ^2 \cdot 5 } =
- \sqrt{ 3 ^2 } \, \sqrt{ 5 } =
- 3 \sqrt{ 5 }$$ |
| ⑤ | Combine like terms |
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