Answer
$$\frac{2\sqrt{7}}{7\sqrt{7}}=\frac{2}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{7}}{7\sqrt{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{7}}{7\sqrt{7}}\frac{\sqrt{7}}{\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{14}{49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 14 : \color{orangered}{ 7 } }{ 49 : \color{orangered}{ 7 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{7}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{7} } \cdot \sqrt{7} = 14 $$ Simplify denominator. $$ \color{blue}{ 7 \sqrt{7} } \cdot \sqrt{7} = 49 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 7 } $. |
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