Question
Answer
$$\dfrac{2\sqrt{11}}{\sqrt{132}}=\dfrac{\sqrt{3}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{11}}{\sqrt{132}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{11}}{\sqrt{132}}\frac{\sqrt{132}}{\sqrt{132}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{44\sqrt{3}}{132} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{3}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{132}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{11} } \cdot \sqrt{132} = 44 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{132} } \cdot \sqrt{132} = 132 $$ |
| ③ | Divide both numerator and denominator by 44. |
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