Answer
$$\frac{\sqrt{77}}{\sqrt{21}}=\frac{\sqrt{33}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{77}}{\sqrt{21}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{77}}{\sqrt{21}}\frac{\sqrt{21}}{\sqrt{21}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7\sqrt{33}}{21} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{33}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{21}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{77} } \cdot \sqrt{21} = 7 \sqrt{33} $$ Simplify denominator. $$ \color{blue}{ \sqrt{21} } \cdot \sqrt{21} = 21 $$ |
| ③ | Divide both numerator and denominator by 7. |
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