\(\sqrt{4+2\sqrt{3}} - \sqrt{4-2\sqrt{3}}\\ =\sqrt{3+2\sqrt{3}+1} - \sqrt{3-2\sqrt{3}+1}\\ =\sqrt{\sqrt3^2+2\sqrt{3}+1^2} - \sqrt{\sqrt3^2-2\sqrt{3}+1^2}\\ =\sqrt{(\sqrt3+1)^2}-\sqrt{(\sqrt3-1)^2}\\ =(\sqrt3+1)-(\sqrt3-1)\\ =\sqrt3 -\sqrt3 + 1 - (-1)\\ =2\)
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