Question
Answer
$$\dfrac{5}{\sqrt{40}}=\dfrac{\sqrt{10}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{\sqrt{40}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 5 }{\sqrt{ 40 }} \times \frac{ \color{orangered}{\sqrt{ 40 }} }{ \color{orangered}{\sqrt{ 40 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{40}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 5 \sqrt{ 4 \cdot 10 }}{ 40 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 5 \cdot 2 \sqrt{ 10 } }{ 40 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{10\sqrt{10}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 10 \sqrt{ 10 } : \color{blue}{ 10 } }{ 40 : \color{blue}{ 10 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{10}}{4}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 40 }}$. |
| ② | In denominator we have $ \sqrt{ 40 } \cdot \sqrt{ 40 } = 40 $. |
| ③ | Simplify $ \sqrt{ 40 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 10 }$. |
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