Question
Answer
$$\sqrt{45}^5=6075\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{45}^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3\sqrt{5})^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6075\sqrt{5}\end{aligned} $$ | |
| ① | $$ \sqrt{45} =
\sqrt{ 3 ^2 \cdot 5 } =
\sqrt{ 3 ^2 } \, \sqrt{ 5 } =
3 \sqrt{ 5 }$$ |
| ② | $$ (3\sqrt{5})^5 =
3^{ 5 } \cdot \sqrt{5} ^ { 5 } =
3^{ 5 } \left( \sqrt{5} ^2 \right)^{ 2 } \cdot \sqrt{5} =
3^{ 5 } \lvert 5 \rvert ^{ 2 } \cdot \sqrt{5} =
6075\sqrt{5} $$ |
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