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