\(\sqrt{6-2\sqrt{2}+\sqrt{21}+\sqrt{18-\sqrt{128}}}=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-2\sqrt{32}}}}=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{\left(4-\sqrt{2}\right)^2}}}=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+4-\sqrt{2}}}=\sqrt{6-2\sqrt{4+2\sqrt{3}}=\sqrt{6-2\sqrt{\left(\sqrt{3}+1\right)^2}}}=\sqrt{6-2\sqrt{3}-2}=\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)