\(A=\sqrt{2}\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4-\sqrt{15}}\)
\(=\sqrt{2}\sqrt{4+\sqrt{15}}\left(\sqrt{5}-\sqrt{3}\right).\left(16-15\right)\)
\(=\sqrt{8+2\sqrt{15}}\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}\left(\sqrt{5}-\sqrt{3}\right)\)
\(=\left(\sqrt{3}+\sqrt{5}\right).\left(\sqrt{5}-\sqrt{3}\right)=5-3=2\)
\(B^2=8+2\sqrt{16-\left(10+2\sqrt{5}\right)}\)
\(=8+2\sqrt{6-2\sqrt{5}}\)
\(=8+2\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(=8+2\sqrt{5}-2=6+2\sqrt{5}\)
Mà \(B>0\) \(\Rightarrow B=\sqrt{6+2\sqrt{5}}=\sqrt{\left(\sqrt{5}-1\right)^2}=\sqrt{5}-1\)
