Question

Rút gọn.

\(A=\left(4\sqrt{3}-4\right)\sqrt{3+\sqrt{5-\sqrt{13+2\sqrt{2}}}}\)

\(B=\sqrt{\sqrt{83-20\sqrt{6}}+\sqrt{62-20\sqrt{6}}}.\sqrt{3\sqrt{3}-3\sqrt{2}}\)

Answer 1

B = \(\sqrt{\sqrt{75-2.2\sqrt{2}.5\sqrt{3}+8}+\sqrt{50-2.2\sqrt{3}.5\sqrt{2}+12}}.\sqrt{3\sqrt{3}-3\sqrt{2}}\)

   = \(\sqrt{\sqrt{\left(5\sqrt{3}-2\sqrt{2}\right)^2}+\sqrt{\left(5\sqrt{2}+2\sqrt{3}\right)^2}}.\sqrt{3\sqrt{3}-3\sqrt{2}}\)

   = \(\sqrt{5\sqrt{3}-2\sqrt{2}+5\sqrt{2}-2\sqrt{3}}.\sqrt{3\sqrt{3}-3\sqrt{2}}\)

   = \(\sqrt{3\sqrt{3}+3\sqrt{2}}.\sqrt{3\sqrt{3}-3\sqrt{2}}=\sqrt{\left(3\sqrt{3}+3\sqrt{2}\right)\left(3\sqrt{3}-3\sqrt{2}\right)}\)

   = \(\sqrt{27-18}=\sqrt{9}=3\)