Answer
$$\frac{4}{\sqrt{160}}=\frac{\sqrt{10}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{\sqrt{160}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 4 }{\sqrt{ 160 }} \times \frac{ \color{orangered}{\sqrt{ 160 }} }{ \color{orangered}{\sqrt{ 160 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{160}}{160} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 4 \sqrt{ 16 \cdot 10 }}{ 160 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 4 \cdot 4 \sqrt{ 10 } }{ 160 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{16\sqrt{10}}{160} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 16 \sqrt{ 10 } : \color{blue}{ 16 } }{ 160 : \color{blue}{ 16 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{10}}{10}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 160 }}$. |
| ② | In denominator we have $ \sqrt{ 160 } \cdot \sqrt{ 160 } = 160 $. |
| ③ | Simplify $ \sqrt{ 160 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 16 }$. |
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