Answer
$$\frac{65}{\sqrt{143}}=\frac{5\sqrt{143}}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{65}{\sqrt{143}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 65 }{\sqrt{ 143 }} \times \frac{ \color{orangered}{\sqrt{ 143 }} }{ \color{orangered}{\sqrt{ 143 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{65\sqrt{143}}{143} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 65 \sqrt{ 143 } : \color{blue}{ 13 } }{ 143 : \color{blue}{ 13 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{143}}{11}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 143 }}$. |
| ② | In denominator we have $ \sqrt{ 143 } \cdot \sqrt{ 143 } = 143 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 13 }$. |
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