Question
Answer
$$\dfrac{6-8\sqrt{2}}{\sqrt{6}}=\dfrac{3\sqrt{6}-8\sqrt{3}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6-8\sqrt{2}}{\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6-8\sqrt{2}}{\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{6}-16\sqrt{3}}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{6}-8\sqrt{3}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 6- 8 \sqrt{2}\right) } \cdot \sqrt{6} = \color{blue}{6} \cdot \sqrt{6}\color{blue}{- 8 \sqrt{2}} \cdot \sqrt{6} = \\ = 6 \sqrt{6}- 16 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{6} } \cdot \sqrt{6} = 6 $$ |
| ③ | Divide both numerator and denominator by 2. |
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