Question
Answer
$$\dfrac{1}{\sqrt{50}}=\dfrac{\sqrt{2}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{\sqrt{50}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 1 }{\sqrt{ 50 }} \times \frac{ \color{orangered}{\sqrt{ 50 }} }{ \color{orangered}{\sqrt{ 50 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1\sqrt{50}}{50} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{50}}{50} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{\sqrt{ 25 \cdot 2 }}{ 50 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{\sqrt{ 25 } \cdot \sqrt{ 2 }}{ 50 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5\sqrt{2}}{50} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 5 \sqrt{ 2 } : \color{blue}{ 5 } }{ 50 : \color{blue}{ 5 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{2}}{10}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 50 }}$. |
| ② | In denominator we have $ \sqrt{ 50 } \cdot \sqrt{ 50 } = 50 $. |
| ③ | Simplify $ \sqrt{ 50 } $. |
| ④ | The square root of $ 25 $ is $ 5 $. |
| ⑤ | Divide both the top and bottom numbers by $ \color{blue}{ 5 }$. |
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