Question
Answer
$$4\sqrt{216}^3=5184\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4\sqrt{216}^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4(6\sqrt{6})^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4\cdot1296\sqrt{6} \xlongequal{ } \\[1 em] & \xlongequal{ }5184\sqrt{6}\end{aligned} $$ | |
| ① | $$ \sqrt{216} =
\sqrt{ 6 ^2 \cdot 6 } =
\sqrt{ 6 ^2 } \, \sqrt{ 6 } =
6 \sqrt{ 6 }$$ |
| ② | $$ (6\sqrt{6})^3 =
6^{ 3 } \cdot \sqrt{6} ^ { 3 } =
6^{ 3 } \sqrt{6} ^2 \cdot \sqrt{6} =
6^{ 3 } \lvert 6 \rvert \cdot \sqrt{6} =
1296\sqrt{6} $$ |
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