Question
Answer
$$\dfrac{2\sqrt{12}}{3\sqrt{54}}=\dfrac{2\sqrt{2}}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{12}}{3\sqrt{54}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{12}}{3\sqrt{54}}\frac{\sqrt{54}}{\sqrt{54}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{36\sqrt{2}}{162} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 36 \sqrt{ 2 } : \color{blue}{ 18 } } { 162 : \color{blue}{ 18 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{2}}{9}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{54}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{12} } \cdot \sqrt{54} = 36 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{54} } \cdot \sqrt{54} = 162 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 18 } $. |
This page was created using
Rationalize Denominator Calculator