Question
Answer
$$7\sqrt{28}^6+4\sqrt{7}^6=155036$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7\sqrt{28}^6+4\sqrt{7}^6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}7(2\sqrt{7})^6+4\sqrt{7}^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}7\cdot21952+4\cdot343 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}155036\end{aligned} $$ | |
| ① | $$ \sqrt{28} =
\sqrt{ 2 ^2 \cdot 7 } =
\sqrt{ 2 ^2 } \, \sqrt{ 7 } =
2 \sqrt{ 7 }$$ |
| ② | $$ (2\sqrt{7})^6 =
2^{ 6 } \cdot \sqrt{7} ^ { 6 } =
2^{ 6 } \left( \sqrt{7} ^2 \right)^{ 3 } =
2^{ 6 } \lvert 7 \rvert ^{ 3 } =
21952 $$$$ \sqrt{7}^6 =
\left( \sqrt{7} ^2 \right)^{ 3 } =
\lvert 7 \rvert ^{ 3 } =
343 $$ |
| ③ | Combine like terms |
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