\(A=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\\ =\left[\left(\sqrt{4+\sqrt{15}}\right)\left(\sqrt{4+\sqrt{15}}\right)\right]\left[\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\right]\sqrt{4-\sqrt{15}}\\ =\left[\left(\sqrt{4+\sqrt{15}}\right)\left(\sqrt{4-\sqrt{15}}\right)\right]\cdot\sqrt{4+\sqrt{15}}\cdot\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\\ =1\cdot\sqrt{8+2\sqrt{15}}\cdot\left(\sqrt{5}-\sqrt{3}\right)\\ =\sqrt{3+2\sqrt{15}+5}\cdot\left(\sqrt{5}-\sqrt{3}\right)\\ =\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}\cdot\left(\sqrt{5}-\sqrt{3}\right)\\ =\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)\\ =5-3\\ =2\)
