Question

упростить:√28+10√3+√28-10√3​

Answer 1

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