Multiply Square Roots: example 9.44

1. ⓐ
   $\begin{array}{cccc}& & & \sqrt{2}·\sqrt{6}\hfill \\ \\ \\ \text{Multiply using the Product Property.}\hfill & & & \sqrt{12}\hfill \\ \\ \\ \text{Simplify the radical.}\hfill & & & \sqrt{4}·\sqrt{3}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & 2\sqrt{3}\hfill \end{array}$
   
   
2. ⓑ
   $\begin{array}{cccc}& & & \left(4\sqrt{3}\right)\left(2\sqrt{12}\right)\hfill \\ \\ \\ \text{Multiply using the Product Property.}\hfill & & & 8\sqrt{36}\hfill \\ \\ \\ \text{Simplify the radical.}\hfill & & & 8·6\hfill \\ \\ \\ \text{Simplify.}\hfill & & & 48\hfill \end{array}$

Notice that in (b) we multiplied the coefficients and multiplied the radicals. Also, we did not simplify $\sqrt{12}$. We waited to get the product and then simplified.