\(\sqrt{2+\sqrt{3}}.\sqrt{\left(2+\sqrt{2+\sqrt{3}}\right).\left(2-\sqrt{2+\sqrt{3}}\right)}\\ \sqrt{2+\sqrt{3}}.\sqrt{4-2-\sqrt{3}}\\ \sqrt{2+\sqrt{3}}.\sqrt{2-\sqrt{3}}\\ \sqrt{\left(2+\sqrt{3}\right).\left(2-\sqrt{3}\right)}\\ \sqrt{4-3}\\ \sqrt{1}\\ 1\)