Question
Answer
$$\sqrt{75}^3=375\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{75}^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(5\sqrt{3})^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}375\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{75} =
\sqrt{ 5 ^2 \cdot 3 } =
\sqrt{ 5 ^2 } \, \sqrt{ 3 } =
5 \sqrt{ 3 }$$ |
| ② | $$ (5\sqrt{3})^3 =
5^{ 3 } \cdot \sqrt{3} ^ { 3 } =
5^{ 3 } \sqrt{3} ^2 \cdot \sqrt{3} =
5^{ 3 } \lvert 3 \rvert \cdot \sqrt{3} =
375\sqrt{3} $$ |
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