Question
Answer
$$3\sqrt{8}^4=192$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\sqrt{8}^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(2\sqrt{2})^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}192\end{aligned} $$ | |
| ① | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ② | $$ (2\sqrt{2})^4 =
2^{ 4 } \cdot \sqrt{2} ^ { 4 } =
2^{ 4 } \left( \sqrt{2} ^2 \right)^{ 2 } =
2^{ 4 } \lvert 2 \rvert ^{ 2 } =
64 $$ |
| ③ | $ 3 \cdot 64 = 192 $ |
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