Question

Вычислите :
√(7+4√3) + √(7-4√3)

Answer 1

$sqrt{7+4 sqrt{3} } + sqrt{7-4 sqrt{3} } = \ = sqrt{4+2*2* sqrt{3}+3 }+sqrt{4-2*2* sqrt{3}+3 } = \ =sqrt{2^2+2*2* sqrt{3}+( sqrt{3})^2 }+sqrt{2^2-2*2* sqrt{3}+( sqrt{3})^2 }= \ =sqrt{( 2+sqrt{3})^2 }+sqrt{(2- sqrt{3})^2 }=|2+ sqrt{3} |+|2- sqrt{3} |= \ =2+ sqrt{3}+|2- sqrt{3} |=(2 textgreater sqrt{3}= 2+ sqrt{3}+2- sqrt{3}=4$