Question
Answer
$$\dfrac{8\sqrt{14}}{12\sqrt{18}}=\dfrac{2\sqrt{7}}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8\sqrt{14}}{12\sqrt{18}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8\sqrt{14}}{12\sqrt{18}}\frac{\sqrt{18}}{\sqrt{18}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{48\sqrt{7}}{216} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 48 \sqrt{ 7 } : \color{blue}{ 24 } } { 216 : \color{blue}{ 24 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{7}}{9}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{18}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 \sqrt{14} } \cdot \sqrt{18} = 48 \sqrt{7} $$ Simplify denominator. $$ \color{blue}{ 12 \sqrt{18} } \cdot \sqrt{18} = 216 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 24 } $. |
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