Question
Answer
$$\dfrac{4\sqrt{6}}{4\sqrt{27}}=\dfrac{\sqrt{2}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{6}}{4\sqrt{27}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{6}}{4\sqrt{27}}\frac{\sqrt{27}}{\sqrt{27}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{36\sqrt{2}}{108} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{27}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{6} } \cdot \sqrt{27} = 36 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{27} } \cdot \sqrt{27} = 108 $$ |
| ③ | Divide both numerator and denominator by 36. |
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