Answer
$$\frac{1}{\sqrt{75}}=\frac{\sqrt{3}}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{\sqrt{75}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 1 }{\sqrt{ 75 }} \times \frac{ \color{orangered}{\sqrt{ 75 }} }{ \color{orangered}{\sqrt{ 75 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1\sqrt{75}}{75} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{75}}{75} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{\sqrt{ 25 \cdot 3 }}{ 75 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{\sqrt{ 25 } \cdot \sqrt{ 3 }}{ 75 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5\sqrt{3}}{75} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 5 \sqrt{ 3 } : \color{blue}{ 5 } }{ 75 : \color{blue}{ 5 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{3}}{15}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 75 }}$. |
| ② | In denominator we have $ \sqrt{ 75 } \cdot \sqrt{ 75 } = 75 $. |
| ③ | Simplify $ \sqrt{ 75 } $. |
| ④ | The square root of $ 25 $ is $ 5 $. |
| ⑤ | Divide both the top and bottom numbers by $ \color{blue}{ 5 }$. |
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