Вычислите : [latex]( \sqrt{5+ \sqrt{21} } + \sqrt{5- \sqrt{21} } )^{2} [/latex]

[latex]( \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 [/latex]