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