Question
Answer
$$\dfrac{-8}{\sqrt{245}}=-\dfrac{8\sqrt{5}}{35}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-8}{\sqrt{245}}& \xlongequal{ }-\frac{8}{\sqrt{245}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}- \, \frac{ 8 }{\sqrt{ 245 }} \times \frac{ \color{orangered}{\sqrt{ 245 }} }{ \color{orangered}{\sqrt{ 245 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{8\sqrt{245}}{245} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}- \, \frac{ 8 \sqrt{ 49 \cdot 5 }}{ 245 } \xlongequal{ } \\[1 em] & \xlongequal{ }- \, \frac{ 8 \cdot 7 \sqrt{ 5 } }{ 245 } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{56\sqrt{5}}{245} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}- \, \frac{ 56 \sqrt{ 5 } : \color{blue}{ 7 } }{ 245 : \color{blue}{ 7 } } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{8\sqrt{5}}{35}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 245 }}$. |
| ② | In denominator we have $ \sqrt{ 245 } \cdot \sqrt{ 245 } = 245 $. |
| ③ | Simplify $ \sqrt{ 245 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 7 }$. |
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