Question

simplify 2 (cube root 40) + 3 (Cube root 625) - 5 (cube root 320)

Answer 1

Dear Student,

$$\begin{gathered} 2\sqrt[3]{40}+3\sqrt[3]{625}-5\sqrt[3]{320} \\ =2\sqrt[3]{2\times 2\times 2\times 5}+3\sqrt[3]{5\times 5\times 5\times 5}-5\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2\times 5} \\ =2\times 2\sqrt[3]{5}+3\times 5\sqrt[3]{5}-5\times 2\times 2\sqrt[3]{5} \\ =4\sqrt[3]{5}+15\sqrt[3]{5}-20\sqrt[3]{5} \\ =\sqrt[3]{5}\left(4+15-20\right) \\ =\mathbf{-}\sqrt[\mathbf{3}]{\mathbf{5}} \end{gathered}$$

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