## Thinking Mathematically (6th Edition)

$\sqrt3 \cdot \sqrt{12} = \sqrt{36} = 6$ $\sqrt3$ and $\sqrt{12}$ are irrational numbers, but 6 is not.
Irrational numbers are not closed with respect to multiplication, as can be seen in the example below: $\sqrt3$ and $\sqrt{12}$ are irrational numbers. However, $\sqrt3 \cdot \sqrt{12} = \sqrt{36}=6$, which is not an irrational number.