Answer
$$\frac{3}{\sqrt{108}}=\frac{\sqrt{3}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{\sqrt{108}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 3 }{\sqrt{ 108 }} \times \frac{ \color{orangered}{\sqrt{ 108 }} }{ \color{orangered}{\sqrt{ 108 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{108}}{108} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 3 \sqrt{ 36 \cdot 3 }}{ 108 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 3 \cdot 6 \sqrt{ 3 } }{ 108 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{18\sqrt{3}}{108} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 18 \sqrt{ 3 } : \color{blue}{ 18 } }{ 108 : \color{blue}{ 18 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{3}}{6}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 108 }}$. |
| ② | In denominator we have $ \sqrt{ 108 } \cdot \sqrt{ 108 } = 108 $. |
| ③ | Simplify $ \sqrt{ 108 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 18 }$. |
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