Question
Answer
$$\dfrac{-5}{\sqrt{20}}=-\dfrac{\sqrt{5}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-5}{\sqrt{20}}& \xlongequal{ }-\frac{5}{\sqrt{20}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}- \, \frac{ 5 }{\sqrt{ 20 }} \times \frac{ \color{orangered}{\sqrt{ 20 }} }{ \color{orangered}{\sqrt{ 20 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{5\sqrt{20}}{20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}- \, \frac{ 5 \sqrt{ 4 \cdot 5 }}{ 20 } \xlongequal{ } \\[1 em] & \xlongequal{ }- \, \frac{ 5 \cdot 2 \sqrt{ 5 } }{ 20 } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{10\sqrt{5}}{20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}- \, \frac{ 10 \sqrt{ 5 } : \color{blue}{ 10 } }{ 20 : \color{blue}{ 10 } } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{\sqrt{5}}{2}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 20 }}$. |
| ② | In denominator we have $ \sqrt{ 20 } \cdot \sqrt{ 20 } = 20 $. |
| ③ | Simplify $ \sqrt{ 20 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 10 }$. |
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