Question
Answer
$$3\cdot\dfrac{\sqrt{2}}{5\sqrt{6}}=\dfrac{\sqrt{3}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{\sqrt{2}}{5\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3 \cdot \frac{2\sqrt{3}}{30} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3 \cdot \frac{\sqrt{3}}{15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{3}}{15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{3}}{5}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{6} = 2 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{6} } \cdot \sqrt{6} = 30 $$ |
| ② | Divide both numerator and denominator by 2. |
| ③ | $$ \color{blue}{ 3 } \cdot \sqrt{3} = 3 \sqrt{3} $$$$ \color{blue}{ 1 } \cdot 15 = 15 $$ |
| ④ | Divide both numerator and denominator by 3. |
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