Answer
$$\frac{64}{\sqrt{48}}=\frac{16\sqrt{3}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{64}{\sqrt{48}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 64 }{\sqrt{ 48 }} \times \frac{ \color{orangered}{\sqrt{ 48 }} }{ \color{orangered}{\sqrt{ 48 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{64\sqrt{48}}{48} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 64 \sqrt{ 16 \cdot 3 }}{ 48 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 64 \cdot 4 \sqrt{ 3 } }{ 48 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{256\sqrt{3}}{48} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 256 \sqrt{ 3 } : \color{blue}{ 16 } }{ 48 : \color{blue}{ 16 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{16\sqrt{3}}{3}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 48 }}$. |
| ② | In denominator we have $ \sqrt{ 48 } \cdot \sqrt{ 48 } = 48 $. |
| ③ | Simplify $ \sqrt{ 48 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 16 }$. |
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