Question
Answer
$$3\sqrt{125}^9=3662109375\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\sqrt{125}^9& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(5\sqrt{5})^9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot1220703125\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ }3662109375\sqrt{5}\end{aligned} $$ | |
| ① | $$ \sqrt{125} =
\sqrt{ 5 ^2 \cdot 5 } =
\sqrt{ 5 ^2 } \, \sqrt{ 5 } =
5 \sqrt{ 5 }$$ |
| ② | $$ (5\sqrt{5})^9 =
5^{ 9 } \cdot \sqrt{5} ^ { 9 } =
5^{ 9 } \left( \sqrt{5} ^2 \right)^{ 4 } \cdot \sqrt{5} =
5^{ 9 } \lvert 5 \rvert ^{ 4 } \cdot \sqrt{5} =
1220703125\sqrt{5} $$ |
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