Question
Answer
$$\dfrac{20}{11\sqrt{13}-\sqrt{7}}=\dfrac{220\sqrt{13}+20\sqrt{7}}{1566}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{20}{11\sqrt{13}-\sqrt{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{20}{11\sqrt{13}-\sqrt{7}}\frac{11\sqrt{13}+\sqrt{7}}{11\sqrt{13}+\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{220\sqrt{13}+20\sqrt{7}}{1573+11\sqrt{91}-11\sqrt{91}-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{220\sqrt{13}+20\sqrt{7}}{1566}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 11 \sqrt{13} + \sqrt{7}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 20 } \cdot \left( 11 \sqrt{13} + \sqrt{7}\right) = \color{blue}{20} \cdot 11 \sqrt{13}+\color{blue}{20} \cdot \sqrt{7} = \\ = 220 \sqrt{13} + 20 \sqrt{7} $$ Simplify denominator. $$ \color{blue}{ \left( 11 \sqrt{13}- \sqrt{7}\right) } \cdot \left( 11 \sqrt{13} + \sqrt{7}\right) = \color{blue}{ 11 \sqrt{13}} \cdot 11 \sqrt{13}+\color{blue}{ 11 \sqrt{13}} \cdot \sqrt{7}\color{blue}{- \sqrt{7}} \cdot 11 \sqrt{13}\color{blue}{- \sqrt{7}} \cdot \sqrt{7} = \\ = 1573 + 11 \sqrt{91}- 11 \sqrt{91}-7 $$ |
| ③ | Simplify numerator and denominator |
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