Question
Answer
$$3\sqrt{252}^5=1143072\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\sqrt{252}^5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(6\sqrt{7})^5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot381024\sqrt{7} \xlongequal{ } \\[1 em] & \xlongequal{ }1143072\sqrt{7}\end{aligned} $$ | |
| ① | $$ \sqrt{252} =
\sqrt{ 6 ^2 \cdot 7 } =
\sqrt{ 6 ^2 } \, \sqrt{ 7 } =
6 \sqrt{ 7 }$$ |
| ② | $$ (6\sqrt{7})^5 =
6^{ 5 } \cdot \sqrt{7} ^ { 5 } =
6^{ 5 } \left( \sqrt{7} ^2 \right)^{ 2 } \cdot \sqrt{7} =
6^{ 5 } \lvert 7 \rvert ^{ 2 } \cdot \sqrt{7} =
381024\sqrt{7} $$ |
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