\(A=\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{\left(4-\sqrt{2}\right)^2}}}\)
\(A=\sqrt{6-2\sqrt{4+\sqrt{12}}}=\sqrt{6-2\sqrt{\left(\sqrt{3}+1\right)^2}}\)
\(A=\sqrt{6-2\left(\sqrt{3}+1\right)}=\sqrt{4-2\sqrt{3}}=\sqrt{3}-1\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}\)
\(B=\sqrt{5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}}=\sqrt{5\sqrt{3}+25-5\sqrt{3}}\)
\(B=\sqrt{25}=5\)