[tex]\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\\ =\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{16-2\sqrt{32}+2}}}\\ =\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+4-\sqrt{2}}}\\ =\sqrt{6-2(\sqrt{3}+1)}=\sqrt{6-2\sqrt{3}-2}=\sqrt{4-2\sqrt{3}}=\sqrt{3}-1[/tex]