Cube Root Calculator
Calculate the cube root of any number instantly. Find the value that, when multiplied by itself three times, equals the given number.
How to Use This Cube Root Calculator
- Enter any real number in the input field.
- Click "Calculate Cube Root" to compute the result.
- View the cube root value and the verification (root × root × root).
Cube Root Formula
For negative numbers, the cube root is also negative. For example, the cube root of −27 is −3 because (−3)³ = −27.
Common Cube Roots
| Number | Cube Root | Verification |
|---|---|---|
| 1 | 1 | 1 × 1 × 1 = 1 |
| 8 | 2 | 2 × 2 × 2 = 8 |
| 27 | 3 | 3 × 3 × 3 = 27 |
| 64 | 4 | 4 × 4 × 4 = 64 |
| 125 | 5 | 5 × 5 × 5 = 125 |
| 216 | 6 | 6 × 6 × 6 = 216 |
| 1000 | 10 | 10 × 10 × 10 = 1000 |
Examples
Cube root of 27:
√³27 = 3 because 3 × 3 × 3 = 27
Cube root of 50:
√³50 ≈ 3.684 because 3.684 × 3.684 × 3.684 ≈ 50
Cube root of −64:
√³(−64) = −4 because (−4) × (−4) × (−4) = −64
Frequently Asked Questions
What is the cube root of a negative number?
Yes, negative numbers have real cube roots. Since multiplying three negative numbers yields a negative result, the cube root of a negative number is always negative. For example, √³(−8) = −2.
How is cube root different from square root?
A square root asks "what number multiplied by itself twice equals x?" while a cube root asks "what number multiplied by itself three times equals x?" Square roots of negative numbers are not real, but cube roots of negative numbers are real.
Can I calculate cube root without a calculator?
For perfect cubes (1, 8, 27, 64, 125, etc.), you can memorize them. For non-perfect cubes, you can use prime factorization or estimation. For example, to find √³50, note that 3³ = 27 and 4³ = 64, so the answer is between 3 and 4.