Answer
$$\frac{1}{\sqrt{90}}=\frac{\sqrt{10}}{30}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{\sqrt{90}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 1 }{\sqrt{ 90 }} \times \frac{ \color{orangered}{\sqrt{ 90 }} }{ \color{orangered}{\sqrt{ 90 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1\sqrt{90}}{90} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{90}}{90} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{\sqrt{ 9 \cdot 10 }}{ 90 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{\sqrt{ 9 } \cdot \sqrt{ 10 }}{ 90 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{3\sqrt{10}}{90} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 3 \sqrt{ 10 } : \color{blue}{ 3 } }{ 90 : \color{blue}{ 3 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{10}}{30}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 90 }}$. |
| ② | In denominator we have $ \sqrt{ 90 } \cdot \sqrt{ 90 } = 90 $. |
| ③ | Simplify $ \sqrt{ 90 } $. |
| ④ | The square root of $ 9 $ is $ 3 $. |
| ⑤ | Divide both the top and bottom numbers by $ \color{blue}{ 3 }$. |
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