Answer
$$\frac{\sqrt{180}-\sqrt{80}}{\sqrt{5}}=2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{180}-\sqrt{80}}{\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{180}-\sqrt{80}}{\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30-20}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 10 : \color{orangered}{ 5 } }{ 5 : \color{orangered}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{180}- \sqrt{80}\right) } \cdot \sqrt{5} = \color{blue}{ \sqrt{180}} \cdot \sqrt{5}\color{blue}{- \sqrt{80}} \cdot \sqrt{5} = \\ = 30-20 $$ Simplify denominator. $$ \color{blue}{ \sqrt{5} } \cdot \sqrt{5} = 5 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 5 } $. |
| ⑤ | Remove 1 from denominator. |
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