Question
Answer
$$\dfrac{2+\sqrt{180}}{-6}=-\dfrac{1+3\sqrt{5}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2+\sqrt{180}}{-6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2+6\sqrt{5}}{-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1+3\sqrt{5}}{-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-\frac{1+3\sqrt{5}}{3}\end{aligned} $$ | |
| ① | $$ \sqrt{180} =
\sqrt{ 6 ^2 \cdot 5 } =
\sqrt{ 6 ^2 } \, \sqrt{ 5 } =
6 \sqrt{ 5 }$$ |
| ② | Divide both numerator and denominator by 2. |
| ③ | Place a negative sign in front of a fraction. |
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