Tap the blue circles to see an explanation.
$$ \begin{aligned}\frac{\sqrt{72}}{40}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ \sqrt{ 36 \cdot 2 } }{ 40 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \sqrt{ 36 } \cdot \sqrt{ 2 } }{ 40 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6\sqrt{2}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 6 \cdot \sqrt{ 2 } : \color{orangered}{ 2 }}{ 40 : \color{orangered}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{2}}{20}\end{aligned} $$ | |
① | Factor out the largest perfect square of 72. ( in this example we factored out $ 36 $ ) |
② | Rewrite $ \sqrt{ 36 \cdot 2 } $ as the product of two radicals. |
③ | The square root of $ 36 $ is $ 6 $. |
④ | Divide numerator and denominator by $ \color{orangered}{ 2 } $. |