Question
Answer
$$\sqrt{512}^3=8192\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{512}^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(16\sqrt{2})^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8192\sqrt{2}\end{aligned} $$ | |
| ① | $$ \sqrt{512} =
\sqrt{ 16 ^2 \cdot 2 } =
\sqrt{ 16 ^2 } \, \sqrt{ 2 } =
16 \sqrt{ 2 }$$ |
| ② | $$ (16\sqrt{2})^3 =
16^{ 3 } \cdot \sqrt{2} ^ { 3 } =
16^{ 3 } \sqrt{2} ^2 \cdot \sqrt{2} =
16^{ 3 } \lvert 2 \rvert \cdot \sqrt{2} =
8192\sqrt{2} $$ |
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