Question
Answer
$$(\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32})^2=200$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32})^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(\sqrt{2}+2\sqrt{2}+3\sqrt{2}+4\sqrt{2})^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(10\sqrt{2})^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}200\end{aligned} $$ | |
| ① | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ② | $$ \sqrt{18} =
\sqrt{ 3 ^2 \cdot 2 } =
\sqrt{ 3 ^2 } \, \sqrt{ 2 } =
3 \sqrt{ 2 }$$ |
| ③ | $$ \sqrt{32} =
\sqrt{ 4 ^2 \cdot 2 } =
\sqrt{ 4 ^2 } \, \sqrt{ 2 } =
4 \sqrt{ 2 }$$ |
| ④ | Combine like terms |
| ⑤ | $$ (10\sqrt{2})^2 =
10^{ 2 } \cdot \sqrt{2} ^ { 2 } =
10^{ 2 } \sqrt{2} ^2 =
10^{ 2 } \lvert 2 \rvert =
200 $$ |
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