Question
Answer
$$\dfrac{17+\sqrt{2}}{18+8\sqrt{15}}=\dfrac{-153+68\sqrt{15}-9\sqrt{2}+4\sqrt{30}}{318}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{17+\sqrt{2}}{18+8\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{17+\sqrt{2}}{18+8\sqrt{15}}\frac{18-8\sqrt{15}}{18-8\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{306-136\sqrt{15}+18\sqrt{2}-8\sqrt{30}}{324-144\sqrt{15}+144\sqrt{15}-960} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{306-136\sqrt{15}+18\sqrt{2}-8\sqrt{30}}{-636} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{153-68\sqrt{15}+9\sqrt{2}-4\sqrt{30}}{-318} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{-153+68\sqrt{15}-9\sqrt{2}+4\sqrt{30}}{318}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 18- 8 \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 17 + \sqrt{2}\right) } \cdot \left( 18- 8 \sqrt{15}\right) = \color{blue}{17} \cdot18+\color{blue}{17} \cdot- 8 \sqrt{15}+\color{blue}{ \sqrt{2}} \cdot18+\color{blue}{ \sqrt{2}} \cdot- 8 \sqrt{15} = \\ = 306- 136 \sqrt{15} + 18 \sqrt{2}- 8 \sqrt{30} $$ Simplify denominator. $$ \color{blue}{ \left( 18 + 8 \sqrt{15}\right) } \cdot \left( 18- 8 \sqrt{15}\right) = \color{blue}{18} \cdot18+\color{blue}{18} \cdot- 8 \sqrt{15}+\color{blue}{ 8 \sqrt{15}} \cdot18+\color{blue}{ 8 \sqrt{15}} \cdot- 8 \sqrt{15} = \\ = 324- 144 \sqrt{15} + 144 \sqrt{15}-960 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
| ⑤ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator