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Cube Root Calculator

Enter a positive or negative value to find its cube root.

3Cube root

Real cube root with perfect-cube and Newton verification

Compute the real cube root for positive or negative values, find the nearest integer cube and show Newton iterations as a numerical check.

—Real cube root
—Nearest integer cube
—Cube-back error
Ready.

Formula and interpretation

∛x is the number that multiplied by itself three times equals x.

Unlike square roots, real cube roots exist for negative values.

Worked check

A simple exact check is ∛27 = 3 because 3 × 3 × 3 = 27. Real cube roots also work for negative numbers: ∛(-8) = -2. That differs from the real square-root rule for negative inputs.

Rule: ∛x is the number that multiplied by itself three times equals x. Unlike square roots, real cube roots exist for negative values. For a final check, estimate the expected size of the answer before copying it, keep units consistent, and round only the displayed result rather than intermediate values. Re-enter one simple case by hand when possible; a result with the wrong sign or order of magnitude usually points to an input or reference-base mistake.

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