Question
Answer
$$3^3\sqrt{80}+2\sqrt{124}^6=27\cdot4\sqrt{5}+3813248$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3^3\sqrt{80}+2\sqrt{124}^6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3^3\cdot4\sqrt{5}+2(2\sqrt{31})^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}27\cdot4\sqrt{5}+2\cdot1906624 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}27\cdot4\sqrt{5}+3813248\end{aligned} $$ | |
| ① | $$ \sqrt{80} =
\sqrt{ 4 ^2 \cdot 5 } =
\sqrt{ 4 ^2 } \, \sqrt{ 5 } =
4 \sqrt{ 5 }$$ |
| ② | $$ \sqrt{124} =
\sqrt{ 2 ^2 \cdot 31 } =
\sqrt{ 2 ^2 } \, \sqrt{ 31 } =
2 \sqrt{ 31 }$$ |
| ③ | $ 3 ^ 3 = 27 $$$ (2\sqrt{31})^6 =
2^{ 6 } \cdot \sqrt{31} ^ { 6 } =
2^{ 6 } \left( \sqrt{31} ^2 \right)^{ 3 } =
2^{ 6 } \lvert 31 \rvert ^{ 3 } =
1906624 $$ |
| ④ | $ 2 \cdot 1906624 = 3813248 $ |
This page was created using
Simplify Radical Expression