Question
Answer
$$\sqrt{\dfrac{192}{216}}=\dfrac{2}{3}\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{192}{216}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{9}\sqrt{72} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2}{3}\sqrt{2}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 8 }{ 9 } } = \frac{ \sqrt{ 8 } } {\sqrt{ 9 }}
= \frac{ \sqrt{ 8 } } {\sqrt{ 9 }} \cdot \frac{ \sqrt{ 9 } } {\sqrt{ 9 }} = \\
= \frac{ \sqrt{ 72 }} { 9 } = \frac{ 1 }{ 9 } \sqrt{ 72 } $$ |
| ② | $$ \frac{ 1 }{ 9 } \sqrt{ 72 } =
\frac{ 1 }{ 9 } \sqrt{ 6 ^2 \cdot 2 } =
\frac{ 1 }{ 9 } \sqrt{ 6 ^2 } \, \sqrt{ 2 } =
\frac{ 1 }{ 9 } \cdot 6 \sqrt{ 2 } =
\frac{ 2 }{ 3 } \sqrt{ 2 } $$ |
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