Question
Answer
$$2\cdot\dfrac{\sqrt{3}}{\sqrt{27}}=\dfrac{2}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{\sqrt{3}}{\sqrt{27}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2\cdot\frac{9}{27} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2 \cdot \frac{ 9 : \color{orangered}{ 9 } }{ 27 : \color{orangered}{ 9 }} \xlongequal{ } \\[1 em] & \xlongequal{ }2\cdot\frac{1}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2}{3}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{3} } \cdot \sqrt{27} = 9 $$ Simplify denominator. $$ \color{blue}{ \sqrt{27} } \cdot \sqrt{27} = 27 $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 9 } $. |
| ③ | Multiply $2$ by $ \dfrac{1}{3} $ to get $ \dfrac{2}{3} $. Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. $$ \begin{aligned} 2 \cdot \frac{1}{3} = \frac{2}{\color{red}{1}} \cdot \frac{1}{3} = \frac{2}{3} \end{aligned} $$ |
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