Đáp án:
`\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}`
`=(\sqrt{2}.(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}))/(\sqrt{2})`
`=(\sqrt{2}.\sqrt{2+\sqrt{3}}-\sqrt{2}.\sqrt{2-\sqrt{3}})/(\sqrt{2})`
`=(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}})/(\sqrt{2})`
`=(\sqrt{3+2\sqrt{3}+1}-\sqrt{3-2\sqrt{3}+1})/(\sqrt{2})`
`=(\sqrt{(\sqrt{3}+1)^2}-\sqrt{(\sqrt{3}-1)^2})/(\sqrt{2})`
`=(|\sqrt{3}+1|-|\sqrt{3}-1|)/(\sqrt{2})`
`=(\sqrt{3}+1-\sqrt{3}+1)/(\sqrt{2})`
`=(2)/(\sqrt{2})`
`=\sqrt{2}`
