`a, = sqrt(5 - 2 sqrt 10 + 2) - sqrt(5 + 2 sqrt 10 + 2)`
`= sqrt 5 - sqrt 2 - sqrt 5 - sqrt 2`
`= -2 sqrt 2`
\(c,=\sqrt{5-2.\sqrt{5.2}+2}-\sqrt{5+2\sqrt{10}+2}\\ =\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\\ =\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}\\ =-2\sqrt{2}\)
\(d,=\sqrt{45+2.3\sqrt{5}.\sqrt{2}+2}-\sqrt{18-2.3\sqrt{2}.\sqrt{5}+5}\\ =\sqrt{\left(3\sqrt{5}+\sqrt{2}\right)^2}-\sqrt{\left(3\sqrt{2}-\sqrt{5}\right)^2}\\ =3\sqrt{5}+\sqrt{2}-3\sqrt{2}+\sqrt{5}\\ =4\sqrt{5}-2\sqrt{2}\)
c: \(=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}=-2\sqrt{2}\)
d: \(=3\sqrt{5}+\sqrt{2}-3\sqrt{2}+\sqrt{5}\)
\(=4\sqrt{5}-2\sqrt{2}\)