Simplify Square Roots: example 9.18

$\begin{array}{cccc}& & & 3+\sqrt{32}\hfill \\ \begin{array}{c}\text{Rewrite the radicand as a product using the}\hfill \\ \text{largest perfect square factor.}\hfill \end{array}\hfill & & & 3+\sqrt{16·2}\hfill \\ \begin{array}{c}\text{Rewrite the radical as the product of two}\hfill \\ \text{radicals.}\hfill \end{array}\hfill & & & 3+\sqrt{16}·\sqrt{2}\hfill \\ \text{Simplify.}\hfill & & & 3+4\sqrt{2}\hfill \end{array}$

The terms are not like and so we cannot add them. Trying to add an integer and a radical is like trying to add an integer and a variable—they are not like terms!