Question
Answer
$$\dfrac{\sqrt{180}}{6}=\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{180}}{6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ \sqrt{ 36 \cdot 5 } }{ 6 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \sqrt{ 36 } \cdot \sqrt{ 5 } }{ 6 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6\sqrt{5}}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 6 \cdot \sqrt{ 5 } : \color{orangered}{ 6 }}{ 6 : \color{orangered}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{5}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }\sqrt{5}\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 180. ( in this example we factored out $ 36 $ ) |
| ② | Rewrite $ \sqrt{ 36 \cdot 5 } $ as the product of two radicals. |
| ③ | The square root of $ 36 $ is $ 6 $. |
| ④ | Divide numerator and denominator by $ \color{orangered}{ 6 } $. |
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