Question
Answer
$$\sqrt{6}\cdot\dfrac{\sqrt{2}}{\sqrt{3}}=2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{6}\cdot\frac{\sqrt{2}}{\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{6}\cdot\frac{\sqrt{6}}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 6 : \color{orangered}{ 3 } }{ 3 : \color{orangered}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{3} = \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \sqrt{3} } \cdot \sqrt{3} = 3 $$ |
| ② | $$ \color{blue}{ \sqrt{6} } \cdot \sqrt{6} = 6 $$$$ \color{blue}{ 1 } \cdot 3 = 3 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 3 } $. |
| ④ | Remove 1 from denominator. |
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