QuickCalculators finds the cube root of a number, the value that cubes back to the input, including a real cube root for negative inputs. Enter a positive or negative value, then read the principal real cube root with a check against cubing.
Cube root is the inverse of cubing. Cross-link the cube page for x³ and the nth-root page when the index is not 3.
Find the cube root of a number
The cube root of a number a is the number r such that r³ = a, written ∛a or a^(1/3). QuickCalculators returns that real cube root for ordinary real inputs and shows the inverse check by cubing the result.
Unlike square roots, every real number has a real cube root because cubing is a one-to-one function from reals to reals. Zero roots to zero. Positive inputs yield positive roots; negative inputs yield negative roots.
Find the cube root of a perfect cube
When the input is a perfect cube, the cube root is an integer. QuickCalculators marks that integer case so classroom tables match the definition. Example: ∛27 = 3 because 3³ = 27. Example: ∛64 = 4. Recognizing perfect cubes speeds mental work; the calculator verifies any claimed integer root by cubing it.
Find the cube root of a negative number
Negative numbers have real cube roots that are negative. QuickCalculators returns that signed root instead of blocking the input the way a principal square-root tool would for negatives. Example: ∛(−8) = −2 because (−2)³ = −8. This is a key difference from even roots.
Written work should keep the minus with the root value, not drop it after the radical.
Simplify a cube root radical
Simplifying a cube root means factoring out perfect-cube factors from the radicand. Write ∛(a·b) as ∛a · ∛b when a is a perfect cube, then evaluate ∛a. QuickCalculators can show that factoring path for integer radicands when simplification is requested.
Example: ∛16 = ∛(8·2) = 2∛2. Example: ∛54 = ∛(27·2) = 3∛2. Factors that are not perfect cubes stay under the radical.
Find the cube root of 27
The fixture evaluates ∛27 on QuickCalculators.
- Ask which number cubes to 27.
- Test 3: 3 × 3 × 3 = 27.
- Report 3 as the cube root and note that 27 is a perfect cube.
Cubing the output recovers 27, confirming the inverse pair with the cube page.
Avoid this common misconception
A frequent error is assuming cube roots of negatives do not exist because square roots of negatives are not real. Cube roots of negatives are real and negative. Saying "you cannot root a negative" without naming the index mixes even and odd roots. QuickCalculators accepts negative inputs for cube roots and returns the signed real value.
Frequently asked questions
How do you find a cube root?
To find a cube root, find the number that multiplies by itself twice more to equal the input. QuickCalculators returns that value for the entered radicand.
What is the cube root of 27?
The cube root of 27 is 3 because 3³ = 27. Entering 27 on this page returns that fixture.
Can you take the cube root of a negative number?
Yes. The real cube root of a negative number is negative. Example: ∛(−8) = −2.
How is a cube root different from a square root?
A cube root uses index 3 and exists for every real input. A principal square root uses index 2 and is not real for negative inputs.
What does it mean to simplify a cube root?
Simplifying a cube root factors perfect cubes out of the radicand. Example: ∛54 = 3∛2.
How do you check a cube root?
To check a cube root, cube the reported root and confirm the product equals the original radicand.
Summary
QuickCalculators returns the real cube root of a number and verifies by cubing. Perfect cubes yield integer roots. Negative radicands yield negative roots. Radical simplification pulls out perfect-cube factors. The fixture ∛27 equals 3. Do not import the "no root of a negative" rule from square roots into cube roots.