Question
Answer
$$\dfrac{8-20}{\sqrt{20}+\sqrt{20}}=\dfrac{-3\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8-20}{\sqrt{20}+\sqrt{20}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-12}{2\sqrt{20}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-12}{2\sqrt{20}}\frac{\sqrt{20}}{\sqrt{20}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-24\sqrt{5}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{ -24 \sqrt{ 5 } : \color{blue}{ 8 } } { 40 : \color{blue}{ 8 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{-3\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{20}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ -12 } \cdot \sqrt{20} = - 24 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{20} } \cdot \sqrt{20} = 40 $$ |
| ④ | Divide numerator and denominator by $ \color{blue}{ 8 } $. |
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