Answer
$$\frac{4-3\sqrt{3}}{4\sqrt{6}}=\frac{4\sqrt{6}-9\sqrt{2}}{24}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4-3\sqrt{3}}{4\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4-3\sqrt{3}}{4\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{6}-9\sqrt{2}}{24}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 4- 3 \sqrt{3}\right) } \cdot \sqrt{6} = \color{blue}{4} \cdot \sqrt{6}\color{blue}{- 3 \sqrt{3}} \cdot \sqrt{6} = \\ = 4 \sqrt{6}- 9 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{6} } \cdot \sqrt{6} = 24 $$ |
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