Answer
$$\sqrt{216}^4=46656$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{216}^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6\sqrt{6})^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}46656\end{aligned} $$ | |
| ① | $$ \sqrt{216} =
\sqrt{ 6 ^2 \cdot 6 } =
\sqrt{ 6 ^2 } \, \sqrt{ 6 } =
6 \sqrt{ 6 }$$ |
| ② | $$ (6\sqrt{6})^4 =
6^{ 4 } \cdot \sqrt{6} ^ { 4 } =
6^{ 4 } \left( \sqrt{6} ^2 \right)^{ 2 } =
6^{ 4 } \lvert 6 \rvert ^{ 2 } =
46656 $$ |
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