Question
Answer
$$\dfrac{1+\sqrt{6}}{3\sqrt{2}}=\dfrac{\sqrt{2}+2\sqrt{3}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1+\sqrt{6}}{3\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1+\sqrt{6}}{3\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{2}+2\sqrt{3}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 1 + \sqrt{6}\right) } \cdot \sqrt{2} = \color{blue}{1} \cdot \sqrt{2}+\color{blue}{ \sqrt{6}} \cdot \sqrt{2} = \\ = \sqrt{2} + 2 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{2} } \cdot \sqrt{2} = 6 $$ |
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