rút gọn biểu thức
\(=\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\cdot\sqrt{5-2\sqrt{6}}\)
\(=\left(\sqrt{6}-2\right)\left(\sqrt{3}-\sqrt{2}\right)\left(5+2\sqrt{6}\right)\)
\(=\left(3\sqrt{2}-2\sqrt{3}-2\sqrt{3}+2\sqrt{2}\right)\cdot\left(5+2\sqrt{6}\right)\)
\(=\left(5\sqrt{2}-4\sqrt{3}\right)\left(5+2\sqrt{6}\right)\)
\(=25\sqrt{2}+20\sqrt{3}-20\sqrt{3}-24\sqrt{2}=\sqrt{2}\)
\(\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\sqrt{5-\sqrt{24}}\)
\(=\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\left(5\sqrt{6}+12-10-4\sqrt{6}\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\left(\sqrt{6}+2\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(=3\sqrt{2}-2\sqrt{3}+2\sqrt{3}-2\sqrt{2}\)
\(=\sqrt{2}\)
