Question
Answer
$$\sqrt{\dfrac{25}{12}}=\dfrac{5}{6}\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{25}{12}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{12}\sqrt{300} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5}{6}\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 25 }{ 12 } } = \frac{ \sqrt{ 25 } } {\sqrt{ 12 }}
= \frac{ \sqrt{ 25 } } {\sqrt{ 12 }} \cdot \frac{ \sqrt{ 12 } } {\sqrt{ 12 }} = \\
= \frac{ \sqrt{ 300 }} { 12 } = \frac{ 1 }{ 12 } \sqrt{ 300 } $$ |
| ② | $$ \frac{ 1 }{ 12 } \sqrt{ 300 } =
\frac{ 1 }{ 12 } \sqrt{ 10 ^2 \cdot 3 } =
\frac{ 1 }{ 12 } \sqrt{ 10 ^2 } \, \sqrt{ 3 } =
\frac{ 1 }{ 12 } \cdot 10 \sqrt{ 3 } =
\frac{ 5 }{ 6 } \sqrt{ 3 } $$ |
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