Answer
$$\frac{1}{\sqrt{27}}=\frac{\sqrt{3}}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{\sqrt{27}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 1 }{\sqrt{ 27 }} \times \frac{ \color{orangered}{\sqrt{ 27 }} }{ \color{orangered}{\sqrt{ 27 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1\sqrt{27}}{27} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{27}}{27} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{\sqrt{ 9 \cdot 3 }}{ 27 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{\sqrt{ 9 } \cdot \sqrt{ 3 }}{ 27 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{3\sqrt{3}}{27} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 3 \sqrt{ 3 } : \color{blue}{ 3 } }{ 27 : \color{blue}{ 3 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{3}}{9}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 27 }}$. |
| ② | In denominator we have $ \sqrt{ 27 } \cdot \sqrt{ 27 } = 27 $. |
| ③ | Simplify $ \sqrt{ 27 } $. |
| ④ | The square root of $ 9 $ is $ 3 $. |
| ⑤ | Divide both the top and bottom numbers by $ \color{blue}{ 3 }$. |
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