Solve simple rational and radical equations and identify extraneous solutions.
Solve a cube-root equation by isolating the radical and cubing both sides
Problem
Solve \(\sqrt[3]{x~-~2}~=~3\).
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What this problem is really about
Match the inverse operation to the radical's index. A cube root is undone by cubing both sides, and unlike a square root it accepts negative as well as positive radicands, so no nonnegative-domain restriction is needed. After the radical is removed, solve the remaining linear equation and verify by taking the cube root in the original form.
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