Question

$\sqrt[3]{73-\sqrt{85-\sqrt[3]{72-\sqrt{66+\sqrt[3]{-8} } } } } =$

Answer 1

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$\sqrt[3]{73-\sqrt{85-\sqrt[3]{72-\sqrt{66+\sqrt[3]{-2^3} } } } }=\\ \\ \sqrt[3]{73-\sqrt{85-\sqrt[3]{72-\sqrt{66-2} } } } =\\ \\ \sqrt[3]{73-\sqrt{85-\sqrt[3]{72-\sqrt{64} } } } =\\ \\ \sqrt[3]{73-\sqrt{85-\sqrt[3]{72-8} } } =\\ \\ \sqrt[3]{73-\sqrt{85-\sqrt[3]{64} } } =\\ \\ \sqrt[3]{73-\sqrt{85-\sqrt[3]{2^6} } } =$

$\sqrt[3]{73-\sqrt{85-4} } =\\ \\ \sqrt[3]{73-\sqrt{81} } =\\ \\ \sqrt[3]{73-9} =\\ \\ \sqrt[3]{64} =\\ \\ \sqrt[3]{2^6} =2^2=\fbox{ 4 }$