Answer
$$\frac{\sqrt{75}}{20}=\frac{\sqrt{3}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{75}}{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ \sqrt{ 25 \cdot 3 } }{ 20 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \sqrt{ 25 } \cdot \sqrt{ 3 } }{ 20 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5\sqrt{3}}{20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 5 \cdot \sqrt{ 3 } : \color{orangered}{ 5 }}{ 20 : \color{orangered}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{3}}{4}\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 75. ( in this example we factored out $ 25 $ ) |
| ② | Rewrite $ \sqrt{ 25 \cdot 3 } $ as the product of two radicals. |
| ③ | The square root of $ 25 $ is $ 5 $. |
| ④ | Divide numerator and denominator by $ \color{orangered}{ 5 } $. |
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Simplify Radical Expression