smc

Square the expression: $(\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}{)}^2=3+\sqrt{2}-2\sqrt{(3+\sqrt{2})(3-\sqrt{2})}+3-2\sqrt{2}=6-2\sqrt{9-8}=6-2\sqrt{1}=4$ $\Rightarrow \sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=\sqrt{4}=2\Rightarrow \boxed{2}$