Question
Answer
$$\sqrt{12}^7=3456\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{12}^7& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2\sqrt{3})^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3456\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{12} =
\sqrt{ 2 ^2 \cdot 3 } =
\sqrt{ 2 ^2 } \, \sqrt{ 3 } =
2 \sqrt{ 3 }$$ |
| ② | $$ (2\sqrt{3})^7 =
2^{ 7 } \cdot \sqrt{3} ^ { 7 } =
2^{ 7 } \left( \sqrt{3} ^2 \right)^{ 3 } \cdot \sqrt{3} =
2^{ 7 } \lvert 3 \rvert ^{ 3 } \cdot \sqrt{3} =
3456\sqrt{3} $$ |
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