Answer
$$\frac{3\sqrt{3}}{\sqrt{12}}=\frac{3}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{3}}{\sqrt{12}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{3}}{\sqrt{12}}\frac{\sqrt{12}}{\sqrt{12}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 18 : \color{orangered}{ 6 } }{ 12 : \color{orangered}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{12}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 \sqrt{3} } \cdot \sqrt{12} = 18 $$ Simplify denominator. $$ \color{blue}{ \sqrt{12} } \cdot \sqrt{12} = 12 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 6 } $. |
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