Question
Answer
$$\sqrt{\dfrac{6}{50}}=\dfrac{1}{5}\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{6}{50}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{25}\sqrt{75} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{5}\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 3 }{ 25 } } = \frac{ \sqrt{ 3 } } {\sqrt{ 25 }}
= \frac{ \sqrt{ 3 } } {\sqrt{ 25 }} \cdot \frac{ \sqrt{ 25 } } {\sqrt{ 25 }} = \\
= \frac{ \sqrt{ 75 }} { 25 } = \frac{ 1 }{ 25 } \sqrt{ 75 } $$ |
| ② | $$ \frac{ 1 }{ 25 } \sqrt{ 75 } =
\frac{ 1 }{ 25 } \sqrt{ 5 ^2 \cdot 3 } =
\frac{ 1 }{ 25 } \sqrt{ 5 ^2 } \, \sqrt{ 3 } =
\frac{ 1 }{ 25 } \cdot 5 \sqrt{ 3 } =
\frac{ 1 }{ 5 } \sqrt{ 3 } $$ |
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