Question
Answer
$$\sqrt{18}^6=5832$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{18}^6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3\sqrt{2})^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5832\end{aligned} $$ | |
| ① | $$ \sqrt{18} =
\sqrt{ 3 ^2 \cdot 2 } =
\sqrt{ 3 ^2 } \, \sqrt{ 2 } =
3 \sqrt{ 2 }$$ |
| ② | $$ (3\sqrt{2})^6 =
3^{ 6 } \cdot \sqrt{2} ^ { 6 } =
3^{ 6 } \left( \sqrt{2} ^2 \right)^{ 3 } =
3^{ 6 } \lvert 2 \rvert ^{ 3 } =
5832 $$ |
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