`(\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}})/(\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}`
`=(\sqrt{1+2\sqrt{2}+2}+\sqrt{1-2\sqrt{2}+2})/(\sqrt{1+2\sqrt{2}+2}-\sqrt{1-2\sqrt{2}+2})`
`=(\sqrt{(1+\sqrt{2})^{2}}+\sqrt{(1-\sqrt{2})^{2}})/(\sqrt{(1+\sqrt{2})^{2}}-\sqrt{(1-\sqrt{2})^{2}})`
`=(|1+\sqrt{2}|+|1-\sqrt{2}|)/(|1+\sqrt{2}|-|1-\sqrt{2}|)`
`=(1+\sqrt{2}+\sqrt{2}-1)/(1+\sqrt{2}-\sqrt{2}+1)`
`=(2\sqrt{2})/2`
`=\sqrt{2}`
