Step-by-step solution
- Write the expression as ∛(27).
- Prime factorisation: 27 = 3 × 3 × 3.
- Group identical factors into sets of three.
- Take one factor from each complete group.
- Round the decimal to 8 selected places.
- Verify by cubing the calculated result.
Calculate a cube root
Formula used
A cube root reverses raising a number to three. Negative numbers keep negative real cube roots. Cubing the result should reproduce the original input exactly.
How to use this calculator
Enter a number, decimal, fraction, or scientific notation. Choose the precision needed for the decimal result. Press calculate to view every supported result format clearly.
- Use values like 27, -64, 0.001, or 1e6.
- Use fractions like 1/8 or -27/64.
- Turn on auto-calculate for faster repeated checks.
- Copy, share, or download the completed calculation.
Cube root examples
| Input | Cube root | Example type |
|---|---|---|
| 27 | 3 | Positive perfect cube |
| -64 | -4 | Negative perfect cube |
| 125 | 5 | Positive perfect cube |
| 1/8 | 0.5 | Fraction |
| 0.001 | 0.1 | Decimal |
| 2 | 1.25992105 | Non-perfect cube |
| 1e6 | 100 | Scientific notation |
Perfect cube reference table
| Integer | Cube | Cube-root statement |
|---|---|---|
| -10 | -1000 | ∛-1000 = -10 |
| -9 | -729 | ∛-729 = -9 |
| -8 | -512 | ∛-512 = -8 |
| -7 | -343 | ∛-343 = -7 |
| -6 | -216 | ∛-216 = -6 |
| -5 | -125 | ∛-125 = -5 |
| -4 | -64 | ∛-64 = -4 |
| -3 | -27 | ∛-27 = -3 |
| -2 | -8 | ∛-8 = -2 |
| -1 | -1 | ∛-1 = -1 |
| 0 | 0 | ∛0 = 0 |
| 1 | 1 | ∛1 = 1 |
| 2 | 8 | ∛8 = 2 |
| 3 | 27 | ∛27 = 3 |
| 4 | 64 | ∛64 = 4 |
| 5 | 125 | ∛125 = 5 |
| 6 | 216 | ∛216 = 6 |
| 7 | 343 | ∛343 = 7 |
| 8 | 512 | ∛512 = 8 |
| 9 | 729 | ∛729 = 9 |
| 10 | 1000 | ∛1000 = 10 |
Recent calculations
Understanding cube roots
A cube root finds one repeated factor used thrice. Unlike square roots, real cube roots accept negative inputs. This makes odd roots useful across many algebra problems.
A perfect cube has an exact integer cube root. The number 27 equals three multiplied three times. Therefore, its real cube root is exactly three today.
Frequently asked questions
What is the cube root of 27?
The cube root of 27 is exactly 3. Three multiplied by itself three times equals 27. Therefore, 27 is a positive perfect cube number.
Why is 27 a perfect cube?
A perfect cube equals an integer raised cubically. Since three cubed equals 27, the condition holds. Its cube root therefore needs no decimal approximation today.
Can cube roots be negative?
Yes, negative numbers have negative real cube roots. For example, the cube root of -64 equals -4. Cubing any negative result returns the original negative number.
Can I enter a fraction?
Yes, enter fractions using a forward slash. The calculator checks for a zero denominator automatically. Perfect-cube fractions can produce exact fractional answers immediately today.
Does scientific notation work?
Yes, values like 1e6 are accepted directly. The parser recognises standard positive and negative exponents. Results also include a scientific notation display for convenience.
What does decimal precision change?
Precision controls displayed digits after the decimal point. It never changes the underlying mathematical cube-root value. Choose more digits when comparing close numerical results carefully.
How is the answer verified?
The calculator multiplies the root by itself thrice. That product should closely match the original input. Small differences may appear from normal floating-point rounding limits.
What is radical form?
Radical form uses the cube-root symbol around input. It preserves the exact operation without forced rounding. Perfect cubes simplify from radical form into integers cleanly.
How can I save my result?
Use CSV for a compact spreadsheet-friendly calculation record. Use PDF for a formatted printable result document. The copy button places one summary onto your clipboard.