Question

Answer 1

a: \(\sqrt[3]{3}\left(5\sqrt[3]{18}-3\sqrt[3]{144}\right)+\sqrt[3]{5}\cdot\sqrt[3]{50}\)

\(=\sqrt[3]{3}\left(5\cdot3\cdot\sqrt[3]{\dfrac{2}{3}}-3\cdot6\cdot\sqrt[3]{\dfrac{2}{3}}\right)+\sqrt[3]{250}\)

\(=\sqrt[3]{3}\cdot\sqrt[3]{\dfrac{2}{3}}\cdot\left(-3\right)+5\sqrt[3]{2}\)

\(=-3\sqrt[3]{2}+5\sqrt[3]{2}=2\sqrt[3]{2}\)

b: \(\left(12\sqrt[3]{2}+\sqrt[3]{16}-2\sqrt[3]{2}\right)\left(5\sqrt[3]{4}-3\sqrt[3]{\dfrac{1}{2}}\right)\)

\(=\left(12\sqrt[3]{2}+2\sqrt[3]{2}-2\sqrt[3]{2}\right)\left(10\sqrt[3]{\dfrac{1}{2}}-3\sqrt[3]{\dfrac{1}{2}}\right)\)

\(=12\sqrt[3]{2}\cdot7\sqrt[3]{\dfrac{1}{2}}=84\)