Answer
$$\frac{2\sqrt{6}}{\sqrt{52}}=\frac{\sqrt{78}}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{6}}{\sqrt{52}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{6}}{\sqrt{52}}\frac{\sqrt{52}}{\sqrt{52}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{78}}{52} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{78}}{13}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{52}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{6} } \cdot \sqrt{52} = 4 \sqrt{78} $$ Simplify denominator. $$ \color{blue}{ \sqrt{52} } \cdot \sqrt{52} = 52 $$ |
| ③ | Divide both numerator and denominator by 4. |
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