The value of \sqrt[3]{x} where x is an integer, is located between 6 and 7 on the number line. What could be the value of x?

Question

The value of
`\sqrt[3]{x}` where x is an integer, is located between 6 and 7 on the number line. What could be the value of x?

Answer 1

Explanation:

The value would be 6.5

Answer 2

`\displaystyle\\6<\sqrt[3]{x}<7~~~\Big|^3\\\\6^3<\Big(\sqrt[3]{x}\Big)^3<7^3\\\\216<x<343\\\\\boxed{x\in\{217,~218,~219,~220,~\cdots~,~340,~341,~342\}}`

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