Question
Answer
$$\dfrac{26}{\sqrt{480}}=\dfrac{13\sqrt{30}}{60}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{26}{\sqrt{480}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 26 }{\sqrt{ 480 }} \times \frac{ \color{orangered}{\sqrt{ 480 }} }{ \color{orangered}{\sqrt{ 480 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{26\sqrt{480}}{480} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 26 \sqrt{ 16 \cdot 30 }}{ 480 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 26 \cdot 4 \sqrt{ 30 } }{ 480 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{104\sqrt{30}}{480} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 104 \sqrt{ 30 } : \color{blue}{ 8 } }{ 480 : \color{blue}{ 8 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{13\sqrt{30}}{60}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 480 }}$. |
| ② | In denominator we have $ \sqrt{ 480 } \cdot \sqrt{ 480 } = 480 $. |
| ③ | Simplify $ \sqrt{ 480 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 8 }$. |
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