\(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}=\sqrt{2-2\sqrt{2.3}+3}+\sqrt{2+2\sqrt{2.3}+3}=\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}=\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}=2\sqrt{3}\)
\(\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}=\sqrt{2-2\sqrt{2.5}+5}+\sqrt{2+2\sqrt{2.5}+5}=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}=\sqrt{5}-\sqrt{2}+\sqrt{5}+\sqrt{2}=2\sqrt{5}\)
\(\sqrt{11+2\sqrt{8}}+\sqrt{11-2\sqrt{8}}\)
Ta có: \(\left(\sqrt{11+2\sqrt{8}}+\sqrt{11-2\sqrt{8}}\right)^2=11+2\sqrt{8}+11-2\sqrt{8}+2\sqrt{\left(11+2\sqrt{8}\right)\left(11-2\sqrt{8}\right)}=22+2\sqrt{121-32}=22+2\sqrt{89}\)
=>\(\sqrt{11+2\sqrt{8}}+\sqrt{11-2\sqrt{8}}=\sqrt{22+2\sqrt{89}}\)
a) \(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}=\left(\sqrt{3}-\sqrt{2}\right)+\left(\sqrt{3}+\sqrt{2}\right)=2\sqrt{3}\)
b) \(\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}=\left(\sqrt{5}-\sqrt{2}\right)+\left(\sqrt{5}+\sqrt{2}\right)=2\sqrt{5}\)
c) \(\sqrt{11+2\sqrt{8}}+\sqrt{11-2\sqrt{8}}=chả-biết-nữa\)
sorry