Question
Answer
$$\dfrac{5}{\sqrt{125}}=\dfrac{\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{\sqrt{125}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 5 }{\sqrt{ 125 }} \times \frac{ \color{orangered}{\sqrt{ 125 }} }{ \color{orangered}{\sqrt{ 125 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{125}}{125} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 5 \sqrt{ 25 \cdot 5 }}{ 125 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 5 \cdot 5 \sqrt{ 5 } }{ 125 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{25\sqrt{5}}{125} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 25 \sqrt{ 5 } : \color{blue}{ 25 } }{ 125 : \color{blue}{ 25 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 125 }}$. |
| ② | In denominator we have $ \sqrt{ 125 } \cdot \sqrt{ 125 } = 125 $. |
| ③ | Simplify $ \sqrt{ 125 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 25 }$. |
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