Question
Answer
$$\dfrac{171}{\sqrt{209}}=\dfrac{9\sqrt{209}}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{171}{\sqrt{209}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 171 }{\sqrt{ 209 }} \times \frac{ \color{orangered}{\sqrt{ 209 }} }{ \color{orangered}{\sqrt{ 209 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{171\sqrt{209}}{209} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 171 \sqrt{ 209 } : \color{blue}{ 19 } }{ 209 : \color{blue}{ 19 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9\sqrt{209}}{11}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 209 }}$. |
| ② | In denominator we have $ \sqrt{ 209 } \cdot \sqrt{ 209 } = 209 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 19 }$. |
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