Answer
$$\frac{8\sqrt{6}}{5\sqrt{24}}=\frac{4}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8\sqrt{6}}{5\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8\sqrt{6}}{5\sqrt{24}}\frac{\sqrt{24}}{\sqrt{24}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{96}{120} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 96 : \color{orangered}{ 24 } }{ 120 : \color{orangered}{ 24 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{24}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 \sqrt{6} } \cdot \sqrt{24} = 96 $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{24} } \cdot \sqrt{24} = 120 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 24 } $. |
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