Question
Answer
$$\dfrac{2\sqrt{8}}{9\sqrt{12}}=\dfrac{2\sqrt{6}}{27}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{8}}{9\sqrt{12}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{8}}{9\sqrt{12}}\frac{\sqrt{12}}{\sqrt{12}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8\sqrt{6}}{108} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 8 \sqrt{ 6 } : \color{blue}{ 4 } } { 108 : \color{blue}{ 4 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{6}}{27}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{12}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{8} } \cdot \sqrt{12} = 8 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 9 \sqrt{12} } \cdot \sqrt{12} = 108 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 4 } $. |
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