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'Cube Roots' printed from https://nrich.maths.org/

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Why do this problem?

It provides experience of using algebra and working with surds. It leads into complex cube roots if you want to explore the patterns arising with those solutions.

Key questions

We have to evaluate

$c^{1\over 3} - d^{1\over 3}$ what are $c^3$, $d^3$, $cd$ and $(c-d)^3$?