Question
Answer
$$\dfrac{8+\sqrt{4}}{8-\sqrt{4}}=\dfrac{5}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8+\sqrt{4}}{8-\sqrt{4}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8+\sqrt{4}}{8-\sqrt{4}}\frac{8+\sqrt{4}}{8+\sqrt{4}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{64+16+16+4}{64+16-16-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{100}{60} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 100 : \color{orangered}{ 20 } }{ 60 : \color{orangered}{ 20 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 8 + \sqrt{4}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 8 + \sqrt{4}\right) } \cdot \left( 8 + \sqrt{4}\right) = \color{blue}{8} \cdot8+\color{blue}{8} \cdot \sqrt{4}+\color{blue}{ \sqrt{4}} \cdot8+\color{blue}{ \sqrt{4}} \cdot \sqrt{4} = \\ = 64 + 16 + 16 + 4 $$ Simplify denominator. $$ \color{blue}{ \left( 8- \sqrt{4}\right) } \cdot \left( 8 + \sqrt{4}\right) = \color{blue}{8} \cdot8+\color{blue}{8} \cdot \sqrt{4}\color{blue}{- \sqrt{4}} \cdot8\color{blue}{- \sqrt{4}} \cdot \sqrt{4} = \\ = 64 + 16-16-4 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 20 } $. |
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