a) \(=\sqrt{4+\sqrt{8}}.\sqrt{2-\sqrt{2}}=\sqrt{2\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}=\sqrt{2.2}=\sqrt{4}=2\)
b) \(=\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{15}-4\right)\sqrt{4+\sqrt{15}}=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{15}-4\right)\sqrt{8+2\sqrt{15}}\)
\(=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{15}-4\right)\sqrt{\left(\sqrt{5}\right)^2+2.\sqrt{5}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{15}-4\right)\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\left(\sqrt{5}+\sqrt{3}\right)^2\left(\sqrt{15}-4\right)=2\left(4+\sqrt{15}\right)\left(\sqrt{15}-4\right)\)
\(=-2\)
