Question

Найдите значение выражения:sqrt(28+10sqrt(3))+sqrt(28-10sqrt(3))

Answer 1

\sqrt{(28+10\sqrt(3))}+\sqrt{(28-10\sqrt(3))}

$\sqrt{(28+10\sqrt3)}+\sqrt{(28-10\sqrt3)}=\\ \\=\sqrt{25+10\sqrt{3}+3}+\sqrt{25-10\sqrt{3}+3}=\\\\=\sqrt{5^2+2*5*\sqrt{3}+(\sqrt{3})^2}+\sqrt{5^2-2*5*\sqrt{3}+(\sqrt{3})^2}=\\\\=\sqrt{(5+\sqrt{3})^2}+\sqrt{(5-\sqrt{3})^2}=\\\\=5+\sqrt{3}+5-\sqrt{3}=10$