Question
Answer
$$\dfrac{13\sqrt{26}}{13-\sqrt{26}}=\dfrac{169\sqrt{26}+338}{143}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{13\sqrt{26}}{13-\sqrt{26}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{13\sqrt{26}}{13-\sqrt{26}}\frac{13+\sqrt{26}}{13+\sqrt{26}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{169\sqrt{26}+338}{169+13\sqrt{26}-13\sqrt{26}-26} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{169\sqrt{26}+338}{143}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 13 + \sqrt{26}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 13 \sqrt{26} } \cdot \left( 13 + \sqrt{26}\right) = \color{blue}{ 13 \sqrt{26}} \cdot13+\color{blue}{ 13 \sqrt{26}} \cdot \sqrt{26} = \\ = 169 \sqrt{26} + 338 $$ Simplify denominator. $$ \color{blue}{ \left( 13- \sqrt{26}\right) } \cdot \left( 13 + \sqrt{26}\right) = \color{blue}{13} \cdot13+\color{blue}{13} \cdot \sqrt{26}\color{blue}{- \sqrt{26}} \cdot13\color{blue}{- \sqrt{26}} \cdot \sqrt{26} = \\ = 169 + 13 \sqrt{26}- 13 \sqrt{26}-26 $$ |
| ③ | Simplify numerator and denominator |
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