What you’ll learn
Solve x³ = p.
Key idea
Cubing preserves sign and gives a unique real inverse, unlike a positive square equation's opposite solution pair.
A real cube equation has one solution; sign is preserved, not reversed or duplicated.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve x³=-125 over the reals. Enter the exact numerical x.
- (-5)×(-5)×(-5)=-125, so x=-5 solves x³=-125.
- Cubing preserves order and sign on the reals; its real inverse is unique. For a missing p, p=(-5)³=-125.
Answer: -5
Quick Check
Evaluate a worked attempt at solve x³ = p, identify the first invalid step, and provide the correction.
Solve x³=-8000: Step 1 finds cube-root magnitude 20 and recognizes the target's sign. Step 2 reverses that sign and reports x=20. Identify the first invalid step and correct x.