Question
Answer
$$\sqrt{112}^4=12544$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{112}^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4\sqrt{7})^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}12544\end{aligned} $$ | |
| ① | $$ \sqrt{112} =
\sqrt{ 4 ^2 \cdot 7 } =
\sqrt{ 4 ^2 } \, \sqrt{ 7 } =
4 \sqrt{ 7 }$$ |
| ② | $$ (4\sqrt{7})^4 =
4^{ 4 } \cdot \sqrt{7} ^ { 4 } =
4^{ 4 } \left( \sqrt{7} ^2 \right)^{ 2 } =
4^{ 4 } \lvert 7 \rvert ^{ 2 } =
12544 $$ |
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