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