\[\boxed{\mathbf{570\ (570).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \sqrt{8 + 2\sqrt{7}} = \sqrt{7 + 2\sqrt{7} + 1} =\]
\[= \sqrt{\left( \sqrt{7} + 1 \right)^{2}} = \sqrt{7} + 1\]
\[2)\ \sqrt{15 + 6\sqrt{6}} = \sqrt{9 + 6\sqrt{6} + 6} =\]
\[= \sqrt{\left( 3 + \sqrt{6} \right)^{2}} = 3 + \sqrt{6}\]
\[3)\ \sqrt{7 + 2\sqrt{10}} =\]
\[= \sqrt{5 + 2\sqrt{10} + 2} =\]
\[= \sqrt{(\sqrt{5} + \sqrt{2})²} = \sqrt{5} + \sqrt{2}\]