Question
Answer
$$\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}=\dfrac{\sqrt{2}+\sqrt{3}+2}{3\sqrt{2}+\sqrt{3}+\sqrt{6}+4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{2}+\sqrt{3}+2}{\sqrt{2}+\sqrt{3}+\sqrt{6}+2\sqrt{2}+4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}+\sqrt{3}+2}{3\sqrt{2}+\sqrt{3}+\sqrt{6}+4}\end{aligned} $$ | |
| ① | $$ \sqrt{4} = 2 $$ |
| ② | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ③ | Simplify numerator and denominator |
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