How to Calculate Cube Root
What is Cube Root?
The cube root of a number x is a value a such that a³ = x. In other words, you are looking for the number that, multiplied by itself three times, gives you x. Cube roots can be positive, negative, or zero, unlike square roots.
Step-by-Step Guide
- 1Express the number as a product of prime factors
- 2Group prime factors into sets of three
- 3Take one factor from each group of three
- 4Multiply the results — that is the cube root
Worked Examples
Input
∛64
Result
4
Because 4 × 4 × 4 = 64
Input
∛-27
Result
−3
Because (−3)³ = −27
Input
∛125
Result
5
Because 5 × 5 × 5 = 125
Input
∛1000
Result
10
Because 10 × 10 × 10 = 1,000
Input
∛10
Result
2.15443…
Not a perfect cube — irrational result
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