Question

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

Answer 1

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

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