Question
Answer
$$\dfrac{2\sqrt{27}}{3\sqrt{45}}=\dfrac{2\sqrt{15}}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{27}}{3\sqrt{45}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{27}}{3\sqrt{45}}\frac{\sqrt{45}}{\sqrt{45}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18\sqrt{15}}{135} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 18 \sqrt{ 15 } : \color{blue}{ 9 } } { 135 : \color{blue}{ 9 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{15}}{15}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{45}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{27} } \cdot \sqrt{45} = 18 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{45} } \cdot \sqrt{45} = 135 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 9 } $. |
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