Đặt : \(A=\sqrt{8+2\sqrt{10+2\sqrt{5}}}-\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
=> \(A^2=16-2\sqrt{8+2\sqrt{10+2\sqrt{5}}}.\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
\(=16-2\sqrt{8^2-4\left(10+2\sqrt{5}\right)}\)
\(=16-2\sqrt{24-8\sqrt{5}}\)
\(=16-2\sqrt{20-2.2\sqrt{5}.2+4}\)
\(=16-2\sqrt{\left(2\sqrt{5}-2\right)^2}\)
\(=16-2\left(2\sqrt{5}-2\right)=20-4\sqrt{5}\)
=> \(A=\sqrt{20-4\sqrt{5}}\)