\(1.\left(2-\sqrt{2}\right)^2+\sqrt{32}\\ =\left(2^2-2\cdot2\cdot\sqrt{2}+\left(\sqrt{2}\right)^2\right)+4\sqrt{2}\\ =\left(4-4\sqrt{2}+2\right)+4\sqrt{2}\\ =6\\ 2.\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\\ =\sqrt{\left(\sqrt{5}\right)^2+2\cdot\sqrt{5}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}\\ =\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\\ =\sqrt{5}+\sqrt{3}-\sqrt{5}+\sqrt{3}\\ =2\sqrt{3}\)
\(\left(2-\sqrt{2}\right)^2+\sqrt{32}\)
\(=4-4\sqrt{2}+2+4\sqrt{2}\)
\(=4+2=6\)
\(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)
\(=\sqrt{5+2\cdot\sqrt{5}\cdot\sqrt{3}+3}-\sqrt{5-2\cdot\sqrt{5}\cdot\sqrt{3}+3}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
\(=\left|\sqrt{5}+\sqrt{3}\right|-\left|\sqrt{5}-\sqrt{3}\right|\)
\(=\sqrt{5}+\sqrt{3}-\sqrt{5}+\sqrt{3}\)
\(=2\sqrt{3}\)