Question
Answer
$$\dfrac{-3\sqrt{6}}{6+\sqrt{5}}=\dfrac{-18\sqrt{6}+3\sqrt{30}}{31}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-3\sqrt{6}}{6+\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-3\sqrt{6}}{6+\sqrt{5}}\frac{6-\sqrt{5}}{6-\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-18\sqrt{6}+3\sqrt{30}}{36-6\sqrt{5}+6\sqrt{5}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-18\sqrt{6}+3\sqrt{30}}{31}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6- \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ - 3 \sqrt{6} } \cdot \left( 6- \sqrt{5}\right) = \color{blue}{- 3 \sqrt{6}} \cdot6\color{blue}{- 3 \sqrt{6}} \cdot- \sqrt{5} = \\ = - 18 \sqrt{6} + 3 \sqrt{30} $$ Simplify denominator. $$ \color{blue}{ \left( 6 + \sqrt{5}\right) } \cdot \left( 6- \sqrt{5}\right) = \color{blue}{6} \cdot6+\color{blue}{6} \cdot- \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot6+\color{blue}{ \sqrt{5}} \cdot- \sqrt{5} = \\ = 36- 6 \sqrt{5} + 6 \sqrt{5}-5 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator