Question
Answer
$$\sqrt{20}^8=160000$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{20}^8& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2\sqrt{5})^8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}160000\end{aligned} $$ | |
| ① | $$ \sqrt{20} =
\sqrt{ 2 ^2 \cdot 5 } =
\sqrt{ 2 ^2 } \, \sqrt{ 5 } =
2 \sqrt{ 5 }$$ |
| ② | $$ (2\sqrt{5})^8 =
2^{ 8 } \cdot \sqrt{5} ^ { 8 } =
2^{ 8 } \left( \sqrt{5} ^2 \right)^{ 4 } =
2^{ 8 } \lvert 5 \rvert ^{ 4 } =
160000 $$ |
This page was created using
Simplify Radical Expression