\[\boxed{\mathbf{515\ (515).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \sqrt{a^{10}} = a^{5},\ \ при\ a \geq 0;\]
\[2)\ \sqrt{a^{10}} = - a^{5},\ \ при\ a < 0;\]
\[3)\ \sqrt{a^{2}} = \left( \sqrt{a} \right)^{2},\ \ для\ a \geq 0;\]
\[4)\ \sqrt{a^{2}} = \left( \sqrt{- a} \right)^{2},\ \ \]
\[при\ a < 0.\]