a: \(A=\sqrt{\left(3-2\sqrt{5}\right)^2}-2\sqrt{\left(1-\sqrt{5}\right)^2}\)
\(=\left|2\sqrt{5}-3\right|-2\left|\sqrt{5}-1\right|\)
\(=2\sqrt{5}-3-2\left(\sqrt{5}-1\right)\)
\(=2\sqrt{5}-3-2\sqrt{5}+2=-1\)
b: \(B=\sqrt{\dfrac{8+\sqrt{15}}{2}}+\sqrt{\dfrac{8-\sqrt{15}}{2}}\)
\(=\sqrt{\dfrac{16+2\sqrt{15}}{4}}+\sqrt{\dfrac{16-2\sqrt{15}}{4}}\)
\(=\dfrac{1}{2}\left(\sqrt{16+2\sqrt{15}}+\sqrt{16-2\sqrt{15}}\right)\)
\(=\dfrac{1}{2}\left(\sqrt{15}+1+\sqrt{15}-1\right)=\dfrac{2\sqrt{15}}{2}=\sqrt{15}\)
c: \(B=\dfrac{3}{\sqrt{7}-2}-\dfrac{8}{3-\sqrt{7}}\)
\(=\dfrac{3\left(\sqrt{7}+2\right)}{3}-\dfrac{8\left(3+\sqrt{7}\right)}{2}\)
\(=\sqrt{7}+2-4\left(3+\sqrt{7}\right)\)
\(=\sqrt{7}+2-12-4\sqrt{7}=-3\sqrt{7}-10\)
d: \(B=\dfrac{5+\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}+1}-\left(\sqrt{3}+\sqrt{5}\right)\)
\(=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}}+\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}-\sqrt{3}-\sqrt[]{5}\)
\(=\sqrt{5}+1+\sqrt{3}-\sqrt{3}-\sqrt{5}\)
=1