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