Question

Решите пожалуста дам20 балов

Answer 1

$\sqrt{11+6\sqrt2}+\sqrt{11-6\sqrt2}=\sqrt{9+6\sqrt2+2}+\sqrt{9-6\sqrt2+2}=\\\\=\sqrt{(3+\sqrt2)^2}+\sqrt{(3-\sqrt2)^2}=3+\sqrt2+3-\sqrt2=3+3=6\\\\\\Otvet:\;6.$

Answer 2

$\sqrt{11+6\sqrt{2} }+\sqrt{11-6\sqrt{2} } =\sqrt{9+2\cdot3\sqrt{2}+2 } +\sqrt{9-2\cdot3\sqrt{2}+2 }=\\\\=\sqrt{3^{2} +2\cdot3\sqrt{2}+(\sqrt{2})^{2}}+\sqrt{3^{2} -2\cdot3\sqrt{2}+(\sqrt{2})^{2}}=\\\\=\sqrt{(3+\sqrt{2})^{2}}+\sqrt{(3-\sqrt{2})^{2}}=|3+\sqrt{2}|+|3-\sqrt{2}|=3+\sqrt{2}+3-\sqrt{2}=\boxed6$