Question
Answer
$$\dfrac{25}{\sqrt{150}}=\dfrac{5\sqrt{6}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{25}{\sqrt{150}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 25 }{\sqrt{ 150 }} \times \frac{ \color{orangered}{\sqrt{ 150 }} }{ \color{orangered}{\sqrt{ 150 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{25\sqrt{150}}{150} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 25 \sqrt{ 25 \cdot 6 }}{ 150 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 25 \cdot 5 \sqrt{ 6 } }{ 150 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{125\sqrt{6}}{150} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 125 \sqrt{ 6 } : \color{blue}{ 25 } }{ 150 : \color{blue}{ 25 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{6}}{6}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 150 }}$. |
| ② | In denominator we have $ \sqrt{ 150 } \cdot \sqrt{ 150 } = 150 $. |
| ③ | Simplify $ \sqrt{ 150 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 25 }$. |
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