Answer
$$\sqrt{112}^3=448\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{112}^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4\sqrt{7})^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}448\sqrt{7}\end{aligned} $$ | |
| ① | $$ \sqrt{112} =
\sqrt{ 4 ^2 \cdot 7 } =
\sqrt{ 4 ^2 } \, \sqrt{ 7 } =
4 \sqrt{ 7 }$$ |
| ② | $$ (4\sqrt{7})^3 =
4^{ 3 } \cdot \sqrt{7} ^ { 3 } =
4^{ 3 } \sqrt{7} ^2 \cdot \sqrt{7} =
4^{ 3 } \lvert 7 \rvert \cdot \sqrt{7} =
448\sqrt{7} $$ |
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