Question
Answer
$$\dfrac{24}{1+\sqrt{17}}=\dfrac{-24+24\sqrt{17}}{16}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{24}{1+\sqrt{17}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{24}{1+\sqrt{17}}\frac{1-\sqrt{17}}{1-\sqrt{17}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24-24\sqrt{17}}{1-\sqrt{17}+\sqrt{17}-17} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{24-24\sqrt{17}}{-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-24+24\sqrt{17}}{16}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 1- \sqrt{17}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 24 } \cdot \left( 1- \sqrt{17}\right) = \color{blue}{24} \cdot1+\color{blue}{24} \cdot- \sqrt{17} = \\ = 24- 24 \sqrt{17} $$ Simplify denominator. $$ \color{blue}{ \left( 1 + \sqrt{17}\right) } \cdot \left( 1- \sqrt{17}\right) = \color{blue}{1} \cdot1+\color{blue}{1} \cdot- \sqrt{17}+\color{blue}{ \sqrt{17}} \cdot1+\color{blue}{ \sqrt{17}} \cdot- \sqrt{17} = \\ = 1- \sqrt{17} + \sqrt{17}-17 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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