\(A=\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2}\)
\(=\sqrt{\frac{6+2\sqrt{5}}{2}}+\sqrt{\frac{14-6\sqrt{5}}{2}}-\sqrt{2}\)
\(=\sqrt{\frac{\left(\sqrt{5}+1\right)^2}{2}}+\sqrt{\frac{\left(3-\sqrt{5}\right)^2}{2}}-\sqrt{2}\)
\(=\frac{\sqrt{5}+1}{\sqrt{2}}+\frac{3-\sqrt{5}}{\sqrt{2}}-\sqrt{2}\)
\(=2\sqrt{2}-\sqrt{2}\)