Question

Помогите решить! ........................

Answer 1

$sqrt{16-6sqrt{7}}+sqrt{11+4sqrt{7}}=sqrt{9-2cdot3sqrt{7}+7}+sqrt{4+2cdot2sqrt{7}+7}=\=sqrt{3^2-2cdot3sqrt{7}+(sqrt{7})^2}+sqrt{2^2+2cdot2sqrt{7}+(sqrt{7})^2}=\=sqrt{(3-sqrt{7})^2}+sqrt{(2+sqrt{7})^2}=|3-sqrt{7}|+2+sqrt{7}=\=3-sqrt{7}+2+sqrt{7}=5$