a. \(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)
=\(8\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}\)
=\(\left(8-2-6\right)\sqrt{5\sqrt{3}}\)
=0
b. \(22\sqrt{40\sqrt{22}}+3\sqrt{5\sqrt{48}}-2\sqrt{\sqrt{75}}-4\sqrt{15\sqrt{27}}\)
=\(88\sqrt{5\sqrt{3}}+6\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-12\sqrt{5\sqrt{3}}\)
=\(80\sqrt{5\sqrt{3}}\)
c. \(2\sqrt{8\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
=\(4\sqrt{2\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}\)
=\(4\sqrt{2\sqrt{3}}-8\sqrt{5\sqrt{3}}\)
d. \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10.\left(2+\sqrt{3}\right)}}}\)
=\(\sqrt{4+\sqrt{5\sqrt{3}-5.\left(5-\sqrt{3}\right)}}\)
=\(\sqrt{4+\sqrt{25}}\)
=\(\sqrt{4+5}=\sqrt{9}=3\)