Answer
$$\frac{\sqrt{64}}{8\sqrt{24}}=\frac{\sqrt{6}}{12}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{64}}{8\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{64}}{8\sqrt{24}}\frac{\sqrt{24}}{\sqrt{24}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{16\sqrt{6}}{192} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{6}}{12}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{24}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{64} } \cdot \sqrt{24} = 16 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 8 \sqrt{24} } \cdot \sqrt{24} = 192 $$ |
| ③ | Divide both numerator and denominator by 16. |
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