Question

Вычислите :
$( sqrt{5+ sqrt{21} } + sqrt{5- sqrt{21} } )^{2}$

Answer 1

$( sqrt{5+ sqrt{21} }+ sqrt{5+ sqrt{21} })^2=\\=(sqrt{5+ sqrt{21} })^2+2*sqrt{5+ sqrt{21} }*sqrt{5- sqrt{21} } +(sqrt{5- sqrt{21} })^2=\\=5+ sqrt{21}+2* sqrt{5^2-( sqrt{21})^2 }+5- sqrt{21}=\\=10+2 sqrt{25-21}=10+2* sqrt{4}=10+2*2=10+4=15$