\(\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right).\sqrt{5-2\sqrt{6}}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)\left(5-2\sqrt{6}\right)^2.\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)^2\left(\sqrt{3}-\sqrt{2}\right)^4.\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right).\left(\sqrt{3}+\sqrt{2}\right).\left(\sqrt{3}-\sqrt{2}\right).\left(\sqrt{3}-\sqrt{2}\right) ^3\)
\(=\left(\sqrt{3}-\sqrt{2}\right)^3\)
\(=\left(\sqrt{3}+\sqrt{2}\right)^2\left(5-2\sqrt{6}\right)^2\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)\left(5-2\sqrt{6}\right)^2\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\left(\sqrt{3}+\sqrt{2}\right)\left(49-20\sqrt{6}\right)\)
\(\)
