Answer
$$\frac{4\sqrt{6}}{4\sqrt{12}}=\frac{\sqrt{2}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{6}}{4\sqrt{12}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{6}}{4\sqrt{12}}\frac{\sqrt{12}}{\sqrt{12}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24\sqrt{2}}{48} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{12}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{6} } \cdot \sqrt{12} = 24 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{12} } \cdot \sqrt{12} = 48 $$ |
| ③ | Divide both numerator and denominator by 24. |
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