Question
Answer
$$\dfrac{\sqrt{180}^7}{4}=8748000\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{180}^7}{4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5832000\sqrt{180}}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{34992000\sqrt{5}}{4} \xlongequal{ } \\[1 em] & \xlongequal{ }8748000\sqrt{5}\end{aligned} $$ | |
| ① | $$ \sqrt{180}^7 =
\left( \sqrt{180} ^2 \right)^{ 3 } \cdot \sqrt{180} =
\lvert 180 \rvert ^{ 3 } \cdot \sqrt{180} =
5832000\sqrt{180} $$ |
| ② | $$ 5832000 \sqrt{180} =
5832000 \sqrt{ 6 ^2 \cdot 5 } =
5832000 \sqrt{ 6 ^2 } \, \sqrt{ 5 } =
5832000 \cdot 6 \sqrt{ 5 } =
34992000 \sqrt{ 5 } $$ |
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