26 БАЛЛОВ!!!СРОЧНО!!! вычислите [latex]( \sqrt[6]{5+2 \sqrt{6} }+ \sqrt[3]{ \sqrt{3}+ \sqrt{2} } )* \sqrt[3]{ \sqrt{2}- \sqrt{3} } [/latex]

[latex]5+2 \sqrt{6} =5+2 \sqrt{2} \sqrt{3} =2+2 \sqrt{2} \sqrt{3} +3= (\sqrt{2})^2+ 2 \sqrt{2} \sqrt{3} +( \sqrt{3} )^2= \\ = ( \sqrt{2}+ \sqrt{3} )^2 \\ \sqrt[6]{5+2 \sqrt{6}}= \sqrt[6]{ ( \sqrt{2}+ \sqrt{3} )^2} = \sqrt[3]{ \sqrt{2}+ \sqrt{3} } \\ (\sqrt[3]{ \sqrt{2}+ \sqrt{3} } + \sqrt[3]{ \sqrt{3} + \sqrt{2} } )* \sqrt[3]{ \sqrt{2} - \sqrt{3} } \\ 2*\sqrt[3]{ \sqrt{2}+ \sqrt{3} }*\sqrt[3]{ \sqrt{2} - \sqrt{3} } =2 \sqrt[3]{( \sqrt{2}+ \sqrt{3})*( \sqrt{2} - \sqrt{3} ) } = \\ = 2* \sqrt[3]{2-3} [/latex]=2*(-1)=-2