Question
Answer
$$\dfrac{14\sqrt{30}}{4\sqrt{54}}=\dfrac{7\sqrt{5}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{14\sqrt{30}}{4\sqrt{54}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{14\sqrt{30}}{4\sqrt{54}}\frac{\sqrt{54}}{\sqrt{54}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{252\sqrt{5}}{216} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 252 \sqrt{ 5 } : \color{blue}{ 36 } } { 216 : \color{blue}{ 36 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{7\sqrt{5}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{54}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 14 \sqrt{30} } \cdot \sqrt{54} = 252 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{54} } \cdot \sqrt{54} = 216 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 36 } $. |
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