Question
Answer
$$\dfrac{9+\sqrt{5}}{\sqrt{13}}=\dfrac{9\sqrt{13}+\sqrt{65}}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9+\sqrt{5}}{\sqrt{13}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9+\sqrt{5}}{\sqrt{13}}\frac{\sqrt{13}}{\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{9\sqrt{13}+\sqrt{65}}{13}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{13}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 9 + \sqrt{5}\right) } \cdot \sqrt{13} = \color{blue}{9} \cdot \sqrt{13}+\color{blue}{ \sqrt{5}} \cdot \sqrt{13} = \\ = 9 \sqrt{13} + \sqrt{65} $$ Simplify denominator. $$ \color{blue}{ \sqrt{13} } \cdot \sqrt{13} = 13 $$ |
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