Answer
$$\frac{\sqrt{6}+4}{\sqrt{50}}=\frac{\sqrt{3}+2\sqrt{2}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{6}+4}{\sqrt{50}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{6}+4}{\sqrt{50}}\frac{\sqrt{50}}{\sqrt{50}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{3}+20\sqrt{2}}{50} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{3}+2\sqrt{2}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{50}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{6} + 4\right) } \cdot \sqrt{50} = \color{blue}{ \sqrt{6}} \cdot \sqrt{50}+\color{blue}{4} \cdot \sqrt{50} = \\ = 10 \sqrt{3} + 20 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \sqrt{50} } \cdot \sqrt{50} = 50 $$ |
| ③ | Divide both numerator and denominator by 10. |
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