What you’ll learn
Evaluate cube roots.
Key idea
Cube roots reverse third powers and retain the sign of a real radicand; they are not division by the degree.
Real cube roots retain radicand sign; an odd root has no nonnegative principal restriction.
Worked example
Enter the exact value or ordered values in the format requested below.
Evaluate real ∛(-125). Enter the exact numerical value.
- (-5)×(-5)×(-5)=-125; hence the real cube root ∛-125=-5.
- A missing radicand is recovered by cubing the output: n=(-5)³=-125; a negative cube has a negative real cube root.
Answer: -5
Quick Check
Evaluate a worked attempt at evaluate cube roots, identify the first invalid step, and provide the correction.
Step 1 identifies -8000 as a perfect integer cube. Step 2 evaluates ∛(-8000) by dividing -8000 by 3. Locate the first invalid step and correct the cube root.