Question
Answer
$$\dfrac{5}{\sqrt{4}+10}=\dfrac{5}{12}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{\sqrt{4}+10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{\sqrt{4}+10}\frac{\sqrt{4}-10}{\sqrt{4}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10-50}{4-20+20-100} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-40}{-96} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{40}{96} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 40 : \color{orangered}{ 8 } }{ 96 : \color{orangered}{ 8 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5}{12}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{4}-10} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( \sqrt{4}-10\right) = \color{blue}{5} \cdot \sqrt{4}+\color{blue}{5} \cdot-10 = \\ = 10-50 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{4} + 10\right) } \cdot \left( \sqrt{4}-10\right) = \color{blue}{ \sqrt{4}} \cdot \sqrt{4}+\color{blue}{ \sqrt{4}} \cdot-10+\color{blue}{10} \cdot \sqrt{4}+\color{blue}{10} \cdot-10 = \\ = 4-20 + 20-100 $$ |
| ③ | Simplify numerator and denominator |
| ④ | cancel two minus signs |
| ⑤ | Divide both the top and bottom numbers by $ \color{orangered}{ 8 } $. |
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