d: \(=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}=-2\sqrt{2}\)
e: \(=\sqrt{25-4\left(\sqrt{5}+1\right)}-2\sqrt{5}\)
\(=\sqrt{25-4\sqrt{5}-4}-2\sqrt{5}\)
\(=2\sqrt{5}-1-2\sqrt{5}=-1\)
\(a,=\sqrt{5-2\sqrt{10}+2}-\sqrt{5+2\sqrt{10}+2}\\ =\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\\ =\left|\sqrt{5}-\sqrt{2}\right|-\left|\sqrt{5}+\sqrt{2}\right|\\ =\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}\\ =-2\sqrt{2}\\ e,=\sqrt{25-4\sqrt{5+2\sqrt{5}+1}}-2\sqrt{5}\\ =\sqrt{25-4\sqrt{\left(\sqrt{5}+1\right)^2}}-2\sqrt{5}\\ =\sqrt{25-4\left(\sqrt{5}+1\right)}-2\sqrt{5}\\ =\sqrt{25-4\sqrt{5}-4}-2\sqrt{2}\\ =\sqrt{21-4\sqrt{5}}-2\sqrt{5}\\ =\sqrt{20-2.2.\sqrt{5}+1}-2\sqrt{5}\\ =\sqrt{\left(2\sqrt{5}-1\right)^2}-2\sqrt{5}\\ =2\sqrt{5}-1-2\sqrt{5}\\ =-1\)
