Question
Answer
$$5\sqrt{224}^7=224788480\sqrt{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{224}^7& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5(4\sqrt{14})^7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5\cdot44957696\sqrt{14} \xlongequal{ } \\[1 em] & \xlongequal{ }224788480\sqrt{14}\end{aligned} $$ | |
| ① | $$ \sqrt{224} =
\sqrt{ 4 ^2 \cdot 14 } =
\sqrt{ 4 ^2 } \, \sqrt{ 14 } =
4 \sqrt{ 14 }$$ |
| ② | $$ (4\sqrt{14})^7 =
4^{ 7 } \cdot \sqrt{14} ^ { 7 } =
4^{ 7 } \left( \sqrt{14} ^2 \right)^{ 3 } \cdot \sqrt{14} =
4^{ 7 } \lvert 14 \rvert ^{ 3 } \cdot \sqrt{14} =
44957696\sqrt{14} $$ |
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