Question

\(\sqrt[3]{3\sqrt{2}+7}-\sqrt[3]{3\sqrt{2}-7}\)

Answer 1

\(A=\sqrt[3]{3\sqrt{2}+7}-\sqrt[3]{3\sqrt{2}-7}\)

=>\(A^3=3\sqrt{2}+7-3\sqrt{2}+7-3\cdot A\cdot\sqrt[3]{18-49}\)

=>\(A^3=14-3\cdot A\cdot\sqrt[3]{-31}\)

=>\(A\simeq3,64\)