Answer
$$\frac{6}{\sqrt{34}}=\frac{3\sqrt{34}}{17}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{\sqrt{34}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 6 }{\sqrt{ 34 }} \times \frac{ \color{orangered}{\sqrt{ 34 }} }{ \color{orangered}{\sqrt{ 34 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{34}}{34} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 6 \sqrt{ 34 } : \color{blue}{ 2 } }{ 34 : \color{blue}{ 2 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{34}}{17}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 34 }}$. |
| ② | In denominator we have $ \sqrt{ 34 } \cdot \sqrt{ 34 } = 34 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 2 }$. |
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