\(Ta\text{ }có:\left(2+\sqrt{3}\right)^2=4+4\sqrt{3}+3=7+4\sqrt{3}\\ \left(\sqrt{2}+\sqrt{6}\right)^2=2+2\sqrt{12}+6=8+4\sqrt{3}\\ Mà\text{ }7+4\sqrt{3}< 8+4\sqrt{3}\\ \Rightarrow\left(2+\sqrt{3}\right)^2< \left(\sqrt{2}+\sqrt{6}\right)^2\\ \Rightarrow2+\sqrt{3}< \sqrt{2}+\sqrt{6}\)