Answer
$$\frac{2\sqrt{6}}{5\sqrt{2}}=\frac{2\sqrt{3}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{6}}{5\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{6}}{5\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{3}}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 4 \sqrt{ 3 } : \color{blue}{ 2 } } { 10 : \color{blue}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{3}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{6} } \cdot \sqrt{2} = 4 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{2} } \cdot \sqrt{2} = 10 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 2 } $. |
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