Question
Answer
$$\dfrac{17.6}{17+\sqrt{325}}=\dfrac{-289+85\sqrt{13}}{36}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{17.6}{17+\sqrt{325}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{17.6}{17+\sqrt{325}}\frac{17-\sqrt{325}}{17-\sqrt{325}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{289-85\sqrt{13}}{289-85\sqrt{13}+85\sqrt{13}-325} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{289-85\sqrt{13}}{-36} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-289+85\sqrt{13}}{36}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 17- \sqrt{325}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 17 } \cdot \left( 17- \sqrt{325}\right) = \color{blue}{17} \cdot17+\color{blue}{17} \cdot- \sqrt{325} = \\ = 289- 85 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ \left( 17 + \sqrt{325}\right) } \cdot \left( 17- \sqrt{325}\right) = \color{blue}{17} \cdot17+\color{blue}{17} \cdot- \sqrt{325}+\color{blue}{ \sqrt{325}} \cdot17+\color{blue}{ \sqrt{325}} \cdot- \sqrt{325} = \\ = 289- 85 \sqrt{13} + 85 \sqrt{13}-325 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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