Question

 

Answer 1

\(C=\sqrt{11+4\sqrt{6}}-\sqrt{5-2\sqrt{6}}\\ C=\sqrt{\left(2\sqrt{2}\right)^2+2\cdot2\sqrt{2}\cdot\sqrt{3}+\sqrt{3}^2}-\sqrt{\sqrt{3}^2-2\cdot\sqrt{3}\cdot\sqrt{2}+\sqrt{2}}\\ C=\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\\ C=\left|2\sqrt{2}+\sqrt{3}\right|-\left|\sqrt{3}-\sqrt{2}\right|\\ C=2\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{2}\\ C=3\sqrt{2}.\)