Question
Answer
$$\dfrac{-8+\sqrt{5}}{6\sqrt{12}}=\dfrac{-8\sqrt{3}+\sqrt{15}}{36}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-8+\sqrt{5}}{6\sqrt{12}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-8+\sqrt{5}}{6\sqrt{12}}\frac{\sqrt{12}}{\sqrt{12}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-16\sqrt{3}+2\sqrt{15}}{72} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-8\sqrt{3}+\sqrt{15}}{36}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{12}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( -8 + \sqrt{5}\right) } \cdot \sqrt{12} = \color{blue}{-8} \cdot \sqrt{12}+\color{blue}{ \sqrt{5}} \cdot \sqrt{12} = \\ = - 16 \sqrt{3} + 2 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ 6 \sqrt{12} } \cdot \sqrt{12} = 72 $$ |
| ③ | Divide both numerator and denominator by 2. |
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