Question
Answer
$$\dfrac{1}{8+\sqrt{4}}=\dfrac{1}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{8+\sqrt{4}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{8+\sqrt{4}}\frac{8-\sqrt{4}}{8-\sqrt{4}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8-2}{64-16+16-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6}{60} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 6 : \color{orangered}{ 6 } }{ 60 : \color{orangered}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 8- \sqrt{4}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 1 } \cdot \left( 8- \sqrt{4}\right) = \color{blue}{1} \cdot8+\color{blue}{1} \cdot- \sqrt{4} = \\ = 8-2 $$ 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}{ 6 } $. |
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