Surds5\sqrt[3]{24}-\sqrt[3]{192}

Question

Surds
`5\sqrt[3]{24}-\sqrt[3]{192}`

Answer 1

6∛3

Explanation:

`\displaystyle 5\sqrt[3]{24}-\sqrt[3]{192}=5\sqrt[3]{2^3\cdot3}-\sqrt[3]{4^3\cdot3}\\\\=(5\cdot2-4)\sqrt[3]{3}=\boxed{6\sqrt[3]{3}}`

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The cubes under each radical can be brought out. Coefficients of like radicals can be combined.