Question
Answer
$$2\sqrt{32}^2=64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\sqrt{32}^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(4\sqrt{2})^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\cdot32 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}64\end{aligned} $$ | |
| ① | $$ \sqrt{32} =
\sqrt{ 4 ^2 \cdot 2 } =
\sqrt{ 4 ^2 } \, \sqrt{ 2 } =
4 \sqrt{ 2 }$$ |
| ② | $$ (4\sqrt{2})^2 =
4^{ 2 } \cdot \sqrt{2} ^ { 2 } =
4^{ 2 } \sqrt{2} ^2 =
4^{ 2 } \lvert 2 \rvert =
32 $$ |
| ③ | $ 2 \cdot 32 = 64 $ |
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