Question
Answer
$$6\sqrt{343}^8=83047723206$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6\sqrt{343}^8& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6(7\sqrt{7})^8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6\cdot13841287201 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}83047723206\end{aligned} $$ | |
| ① | $$ \sqrt{343} =
\sqrt{ 7 ^2 \cdot 7 } =
\sqrt{ 7 ^2 } \, \sqrt{ 7 } =
7 \sqrt{ 7 }$$ |
| ② | $$ (7\sqrt{7})^8 =
7^{ 8 } \cdot \sqrt{7} ^ { 8 } =
7^{ 8 } \left( \sqrt{7} ^2 \right)^{ 4 } =
7^{ 8 } \lvert 7 \rvert ^{ 4 } =
13841287201 $$ |
| ③ | $ 6 \cdot 13841287201 = 83047723206 $ |
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