Question
Answer
$$\dfrac{4+2\sqrt{3}}{5\sqrt{4}}=\dfrac{2+\sqrt{3}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4+2\sqrt{3}}{5\sqrt{4}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4+2\sqrt{3}}{5\sqrt{4}}\frac{\sqrt{4}}{\sqrt{4}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8+4\sqrt{3}}{20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2+\sqrt{3}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{4}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 4 + 2 \sqrt{3}\right) } \cdot \sqrt{4} = \color{blue}{4} \cdot \sqrt{4}+\color{blue}{ 2 \sqrt{3}} \cdot \sqrt{4} = \\ = 8 + 4 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{4} } \cdot \sqrt{4} = 20 $$ |
| ③ | Divide both numerator and denominator by 4. |
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