Question
Answer
$$\dfrac{\sqrt{6}}{\sqrt{8}-\sqrt{3}}=\dfrac{4\sqrt{3}+3\sqrt{2}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{6}}{\sqrt{8}-\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{6}}{\sqrt{8}-\sqrt{3}}\frac{\sqrt{8}+\sqrt{3}}{\sqrt{8}+\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{3}+3\sqrt{2}}{8+2\sqrt{6}-2\sqrt{6}-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{3}+3\sqrt{2}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8} + \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{6} } \cdot \left( \sqrt{8} + \sqrt{3}\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{8}+\color{blue}{ \sqrt{6}} \cdot \sqrt{3} = \\ = 4 \sqrt{3} + 3 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{8}- \sqrt{3}\right) } \cdot \left( \sqrt{8} + \sqrt{3}\right) = \color{blue}{ \sqrt{8}} \cdot \sqrt{8}+\color{blue}{ \sqrt{8}} \cdot \sqrt{3}\color{blue}{- \sqrt{3}} \cdot \sqrt{8}\color{blue}{- \sqrt{3}} \cdot \sqrt{3} = \\ = 8 + 2 \sqrt{6}- 2 \sqrt{6}-3 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator