How this calculator works
Simplifying a cube root means removing perfect-cube factors. Factor the number, then for every prime whose exponent reaches 3 move one copy outside the root and subtract 3 from the exponent. For example 40 = 2³ × 5, so ∛40 = 2∛5. A negative input keeps its sign: the coefficient outside the root becomes negative, because an odd root of a negative number is negative.
Formula
∛(k³m) = k∛m. The process repeats until every remaining prime exponent inside the root is 1 or 2, which guarantees the radicand has no perfect-cube factor.
Worked example
∛40 = 2∛5, because 40 = 8 × 5. Likewise ∛81 = ∛(27 × 3) = 3∛3, and ∛-40 = -2∛5. A perfect cube such as 125 = 5³ simplifies all the way to 5.
Advertisement
Frequently asked questions
How is simplifying a cube root different from a square root?
A square root removes factors that appear twice; a cube root removes factors that appear three times. That means a square root can never be pulled from a prime that appears once, while a cube root needs exponent 3, so fewer numbers simplify fully.
Can the number inside the root be negative?
No. After moving the sign to the coefficient, the remaining radicand is positive. That convention keeps -2∛5 readable instead of writing the minus sign inside a cube root.
What if the number is already a perfect cube?
Then the inside radicand is 1 and the answer is a whole number. For example ∛64 = 4 and ∛-27 = -3.
Is the decimal value exact?
No. Cube roots of numbers that are not perfect cubes are irrational, so the decimal is rounded. The exact form beside it is the precise answer.