\(\sqrt{7+2\sqrt{12}}-\sqrt{5-2\sqrt{6}}\\ =\sqrt{3+2.\sqrt{3}\sqrt{4}+4}-\sqrt{2-2\sqrt{2}.\sqrt{3}+3}\\ =\sqrt{\left(\sqrt{3}+\sqrt{4}\right)^2}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\\ =\left|\sqrt{3}+\sqrt{4}\right|-\left|\sqrt{2}-\sqrt{3}\right|\\ =\sqrt{3}+\sqrt{4}-\left(\sqrt{3}-\sqrt{2}\right)\)
(vì \(\sqrt{3}>\sqrt{2}\))
\(=\sqrt{3}+\sqrt{4}-\sqrt{3}+\sqrt{2}=2+\sqrt{2}\)
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