Answer
$$\frac{5\sqrt{5}}{4\sqrt{15}}=\frac{5\sqrt{3}}{12}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5\sqrt{5}}{4\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5\sqrt{5}}{4\sqrt{15}}\frac{\sqrt{15}}{\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{25\sqrt{3}}{60} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 25 \sqrt{ 3 } : \color{blue}{ 5 } } { 60 : \color{blue}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{3}}{12}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 \sqrt{5} } \cdot \sqrt{15} = 25 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{15} } \cdot \sqrt{15} = 60 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 5 } $. |
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