Answer
$$\frac{33}{\sqrt{11}}=3\sqrt{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{33}{\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 33 }{\sqrt{ 11 }} \times \frac{ \color{orangered}{\sqrt{ 11 }} }{ \color{orangered}{\sqrt{ 11 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{33\sqrt{11}}{11} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 33 \sqrt{ 11 } : \color{blue}{ 11 } }{ 11 : \color{blue}{ 11 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{11}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }3\sqrt{11}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 11 }}$. |
| ② | In denominator we have $ \sqrt{ 11 } \cdot \sqrt{ 11 } = 11 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 11 }$. |
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