Answer
$$\frac{7}{\sqrt{7}}=\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7}{\sqrt{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 7 }{\sqrt{ 7 }} \times \frac{ \color{orangered}{\sqrt{ 7 }} }{ \color{orangered}{\sqrt{ 7 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7\sqrt{7}}{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 7 \sqrt{ 7 } : \color{blue}{ 7 } }{ 7 : \color{blue}{ 7 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{7}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }\sqrt{7}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 7 }}$. |
| ② | In denominator we have $ \sqrt{ 7 } \cdot \sqrt{ 7 } = 7 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 7 }$. |
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