\[\begin{array}{l}1){\text{ }}\sqrt {\sqrt[3]{{6 + 2\sqrt 5 }}} = \sqrt[3]{{\sqrt {6 + 2\sqrt 5 } }} = \sqrt[3]{{\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} }} = \sqrt[3]{{\sqrt 5 + 1}}\\2){\text{ }}\sqrt[3]{{1 - \sqrt 5 }} \cdot \sqrt {\sqrt[3]{{6 + 2\sqrt 5 }}} = \sqrt[3]{{1 - \sqrt 5 }} \cdot \sqrt[3]{{1 + \sqrt 5 }} = \\\sqrt[3]{{\left( {1 - \sqrt 5 } \right)\left( {1 + \sqrt 5 } \right)}} = \sqrt[3]{{1 - 5}} = \sqrt[3]{{ - 4}} = - \sqrt[3]{4}\end{array}\]

\[ - \sqrt[3]{4}\]