Question
Answer
$$\dfrac{8}{-\sqrt{10}+\sqrt{5}}=\dfrac{-8\sqrt{10}-8\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8}{-\sqrt{10}+\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8}{-\sqrt{10}+\sqrt{5}}\frac{-\sqrt{10}-\sqrt{5}}{-\sqrt{10}-\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-8\sqrt{10}-8\sqrt{5}}{10+5\sqrt{2}-5\sqrt{2}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-8\sqrt{10}-8\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ - \sqrt{10}- \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 } \cdot \left( - \sqrt{10}- \sqrt{5}\right) = \color{blue}{8} \cdot- \sqrt{10}+\color{blue}{8} \cdot- \sqrt{5} = \\ = - 8 \sqrt{10}- 8 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( - \sqrt{10} + \sqrt{5}\right) } \cdot \left( - \sqrt{10}- \sqrt{5}\right) = \color{blue}{- \sqrt{10}} \cdot- \sqrt{10}\color{blue}{- \sqrt{10}} \cdot- \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot- \sqrt{10}+\color{blue}{ \sqrt{5}} \cdot- \sqrt{5} = \\ = 10 + 5 \sqrt{2}- 5 \sqrt{2}-5 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator