Answer
$$\frac{5\sqrt{3}}{2\sqrt{75}}=\frac{1}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5\sqrt{3}}{2\sqrt{75}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5\sqrt{3}}{2\sqrt{75}}\frac{\sqrt{75}}{\sqrt{75}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{75}{150} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 75 : \color{orangered}{ 75 } }{ 150 : \color{orangered}{ 75 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{75}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 \sqrt{3} } \cdot \sqrt{75} = 75 $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{75} } \cdot \sqrt{75} = 150 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 75 } $. |
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