Answer
$$\frac{3+\sqrt{6}}{4\sqrt{3}}=\frac{\sqrt{3}+\sqrt{2}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3+\sqrt{6}}{4\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3+\sqrt{6}}{4\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{3}+3\sqrt{2}}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{3}+\sqrt{2}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3 + \sqrt{6}\right) } \cdot \sqrt{3} = \color{blue}{3} \cdot \sqrt{3}+\color{blue}{ \sqrt{6}} \cdot \sqrt{3} = \\ = 3 \sqrt{3} + 3 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{3} } \cdot \sqrt{3} = 12 $$ |
| ③ | Divide both numerator and denominator by 3. |
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