Tap the blue circles to see an explanation.
$$ \begin{aligned}\sqrt{2}\cdot\sqrt{10}& \xlongequal{ }\sqrt{20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \sqrt{ 4 \cdot 5 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}} \sqrt{ 4 } \cdot \sqrt{ 5 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2\sqrt{5}\end{aligned} $$ | |
① | Factor out the largest perfect square of 20. ( in this example we factored out $ 4 $ ) |
② | Rewrite $ \sqrt{ 4 \cdot 5 } $ as the product of two radicals. |
③ | The square root of $ 4 $ is $ 2 $. |