Answer
$$2\cdot\frac{\sqrt{24}}{\sqrt{48}}=\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{\sqrt{24}}{\sqrt{48}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2 \cdot \frac{24\sqrt{2}}{48} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2 \cdot \frac{\sqrt{2}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{2}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{2}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }\sqrt{2}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{24} } \cdot \sqrt{48} = 24 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \sqrt{48} } \cdot \sqrt{48} = 48 $$ |
| ② | Divide both numerator and denominator by 24. |
| ③ | $$ \color{blue}{ 2 } \cdot \sqrt{2} = 2 \sqrt{2} $$$$ \color{blue}{ 1 } \cdot 2 = 2 $$ |
| ④ | Divide both numerator and denominator by 2. |
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