Question
Answer
$$\dfrac{2\sqrt{5}}{\sqrt{6}+2}=\sqrt{30}-2\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{5}}{\sqrt{6}+2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{5}}{\sqrt{6}+2}\frac{\sqrt{6}-2}{\sqrt{6}-2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{30}-4\sqrt{5}}{6-2\sqrt{6}+2\sqrt{6}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{30}-4\sqrt{5}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{30}-2\sqrt{5}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\sqrt{30}-2\sqrt{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}-2} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{5} } \cdot \left( \sqrt{6}-2\right) = \color{blue}{ 2 \sqrt{5}} \cdot \sqrt{6}+\color{blue}{ 2 \sqrt{5}} \cdot-2 = \\ = 2 \sqrt{30}- 4 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{6} + 2\right) } \cdot \left( \sqrt{6}-2\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot-2+\color{blue}{2} \cdot \sqrt{6}+\color{blue}{2} \cdot-2 = \\ = 6- 2 \sqrt{6} + 2 \sqrt{6}-4 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
| ⑤ | Remove 1 from denominator. |
This page was created using
Rationalize Denominator Calculator