Question
Answer
$$\sqrt{50}^7=625000\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{50}^7& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(5\sqrt{2})^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}625000\sqrt{2}\end{aligned} $$ | |
| ① | $$ \sqrt{50} =
\sqrt{ 5 ^2 \cdot 2 } =
\sqrt{ 5 ^2 } \, \sqrt{ 2 } =
5 \sqrt{ 2 }$$ |
| ② | $$ (5\sqrt{2})^7 =
5^{ 7 } \cdot \sqrt{2} ^ { 7 } =
5^{ 7 } \left( \sqrt{2} ^2 \right)^{ 3 } \cdot \sqrt{2} =
5^{ 7 } \lvert 2 \rvert ^{ 3 } \cdot \sqrt{2} =
625000\sqrt{2} $$ |
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