Question
Answer
$$\sqrt{40}^{11}=204800000\sqrt{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{40}^{11}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2\sqrt{10})^{11} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}204800000\sqrt{10}\end{aligned} $$ | |
| ① | $$ \sqrt{40} =
\sqrt{ 2 ^2 \cdot 10 } =
\sqrt{ 2 ^2 } \, \sqrt{ 10 } =
2 \sqrt{ 10 }$$ |
| ② | $$ (2\sqrt{10})^{11} =
2^{ 11 } \cdot \sqrt{10} ^ { 11 } =
2^{ 11 } \left( \sqrt{10} ^2 \right)^{ 5 } \cdot \sqrt{10} =
2^{ 11 } \lvert 10 \rvert ^{ 5 } \cdot \sqrt{10} =
204800000\sqrt{10} $$ |
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