[tex]\displaystyle\bf\\\sqrt[3]{\sqrt{3} -\sqrt{2} } \cdot \sqrt[6]{5+2\sqrt{6} } =\sqrt[6]{(\sqrt{3} -\sqrt{2} )^{2} } \cdot \sqrt[6]{5+2\sqrt{6} } =\\\\\\=\sqrt[6]{3-2\sqrt{6} +2} \cdot \sqrt[6]{5+2\sqrt{6} } =\sqrt[6]{5-2\sqrt{6} } \cdot \sqrt[6]{5+2\sqrt{6} } =\\\\\\=\sqrt[6]{(5+2\sqrt{6} )\cdot(5-2\sqrt{6} )} =\sqrt[6]{5^{2} -(2\sqrt{6} )^{2} } =\\\\\\=\sqrt[6]{25-24} =\sqrt[6]{1} =1[/tex]