a) A = \(\sqrt{3+\sqrt{5+2\sqrt{3}}}.\sqrt{3-\sqrt{5+2\sqrt{3}}}\)
= \(\sqrt{\left(3+\sqrt{5+2\sqrt{3}}\right)\left(3-\sqrt{5+2\sqrt{3}}\right)}\)
= \(\sqrt{3^2-\left(\sqrt{5+2\sqrt{3}}\right)^2}\)
= \(\sqrt{9-5-2\sqrt{3}}\)
= \(\sqrt{4-2\sqrt{3}}\)
= \(\sqrt{\left(\sqrt{3}-1\right)^2}\)
= \(\sqrt{3}-1\)
b) B = \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
= \(\sqrt{4+\sqrt{4}.\sqrt{2}}.\sqrt{\left(2+\sqrt{2+\sqrt{2}}\right) \left(2-\sqrt{2+\sqrt{2}}\right)}\)
= \(\sqrt{4+2\sqrt{2}}.\sqrt{2^2-\left(\sqrt{2+\sqrt{2}}\right)^2}\)
= \(\sqrt{2\left(2+\sqrt{2}\right)}.\sqrt{2-\sqrt{2}}\)
= \(\sqrt{2\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}\)
= \(\sqrt{2.2}=2\)
