Question

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

Answer 1

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