Question
Answer
$$\dfrac{2+\sqrt{10}}{\sqrt{6}}=\dfrac{\sqrt{6}+\sqrt{15}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2+\sqrt{10}}{\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2+\sqrt{10}}{\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{6}+2\sqrt{15}}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{6}+\sqrt{15}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 2 + \sqrt{10}\right) } \cdot \sqrt{6} = \color{blue}{2} \cdot \sqrt{6}+\color{blue}{ \sqrt{10}} \cdot \sqrt{6} = \\ = 2 \sqrt{6} + 2 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \sqrt{6} } \cdot \sqrt{6} = 6 $$ |
| ③ | Divide both numerator and denominator by 2. |
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