Question
Answer
$$\dfrac{\sqrt{33}-\sqrt{77}}{\sqrt{77}}=\dfrac{\sqrt{21}-7}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{33}-\sqrt{77}}{\sqrt{77}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{33}-\sqrt{77}}{\sqrt{77}}\frac{\sqrt{77}}{\sqrt{77}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{11\sqrt{21}-77}{77} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{21}-7}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{77}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{33}- \sqrt{77}\right) } \cdot \sqrt{77} = \color{blue}{ \sqrt{33}} \cdot \sqrt{77}\color{blue}{- \sqrt{77}} \cdot \sqrt{77} = \\ = 11 \sqrt{21}-77 $$ Simplify denominator. $$ \color{blue}{ \sqrt{77} } \cdot \sqrt{77} = 77 $$ |
| ③ | Divide both numerator and denominator by 11. |
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