Question
Answer
$$\dfrac{-6}{8+\sqrt{5}}=\dfrac{-48+6\sqrt{5}}{59}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-6}{8+\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-6}{8+\sqrt{5}}\frac{8-\sqrt{5}}{8-\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-48+6\sqrt{5}}{64-8\sqrt{5}+8\sqrt{5}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-48+6\sqrt{5}}{59}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 8- \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -6 } \cdot \left( 8- \sqrt{5}\right) = \color{blue}{-6} \cdot8\color{blue}{-6} \cdot- \sqrt{5} = \\ = -48 + 6 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( 8 + \sqrt{5}\right) } \cdot \left( 8- \sqrt{5}\right) = \color{blue}{8} \cdot8+\color{blue}{8} \cdot- \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot8+\color{blue}{ \sqrt{5}} \cdot- \sqrt{5} = \\ = 64- 8 \sqrt{5} + 8 \sqrt{5}-5 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator