Question

find the value of $\sqrt[3]{339 + \sqrt[3]{32 \sqrt[3]{8} } }$

Answer 1

$\sqrt[3]{339 + \sqrt[3]{32 \sqrt[3]{8} } } \\ \sqrt[3]{339 + \sqrt[3]{32 \times 2} } \\ \sqrt[3]{339 + \sqrt[3]{64} } \\ \sqrt[3]{339 + 4 } \\ \sqrt[3]{343} \\ = 7$