Answer
$$2\sqrt{50}-\sqrt{32}+\sqrt{72}-2\sqrt{8}=8\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\sqrt{50}-\sqrt{32}+\sqrt{72}-2\sqrt{8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}10\sqrt{2}-4\sqrt{2}+6\sqrt{2}-4\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}8\sqrt{2}\end{aligned} $$ | |
| ① | $$ 2 \sqrt{50} =
2 \sqrt{ 5 ^2 \cdot 2 } =
2 \sqrt{ 5 ^2 } \, \sqrt{ 2 } =
2 \cdot 5 \sqrt{ 2 } =
10 \sqrt{ 2 } $$ |
| ② | $$ - \sqrt{32} =
- \sqrt{ 4 ^2 \cdot 2 } =
- \sqrt{ 4 ^2 } \, \sqrt{ 2 } =
- 4 \sqrt{ 2 }$$ |
| ③ | $$ \sqrt{72} =
\sqrt{ 6 ^2 \cdot 2 } =
\sqrt{ 6 ^2 } \, \sqrt{ 2 } =
6 \sqrt{ 2 }$$ |
| ④ | $$ - 2 \sqrt{8} =
-2 \sqrt{ 2 ^2 \cdot 2 } =
-2 \sqrt{ 2 ^2 } \, \sqrt{ 2 } =
-2 \cdot 2 \sqrt{ 2 } =
-4 \sqrt{ 2 } $$ |
| ⑤ | Combine like terms |
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