Answer
$$\frac{4}{\sqrt{54}}=\frac{2\sqrt{6}}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{\sqrt{54}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 4 }{\sqrt{ 54 }} \times \frac{ \color{orangered}{\sqrt{ 54 }} }{ \color{orangered}{\sqrt{ 54 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{54}}{54} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 4 \sqrt{ 9 \cdot 6 }}{ 54 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 4 \cdot 3 \sqrt{ 6 } }{ 54 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{12\sqrt{6}}{54} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 12 \sqrt{ 6 } : \color{blue}{ 6 } }{ 54 : \color{blue}{ 6 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{6}}{9}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 54 }}$. |
| ② | In denominator we have $ \sqrt{ 54 } \cdot \sqrt{ 54 } = 54 $. |
| ③ | Simplify $ \sqrt{ 54 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 6 }$. |
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