Cube Root Calculator
The cube root of a whole number, a decimal or a fraction: the exact form with triples of prime factors taken out of the root, and the decimal value
Cube Root Calculator
Cube Root
∛N is the number whose cube is N. There is exactly one for every N, and for a negative N it is negative.
Example: ∛54
∛54 = 3∛2 ≈ 3.7798
- Prime factors
- 54 = 2 × (3 × 3 × 3) = 2 × 3³
- Take out of the root
- ∛54 = ∛(3³ × 2) = 3∛2
- Between cubes
- 3³ = 27 < 54 < 64 = 4³, so 3 < ∛54 < 4 and ∛54 ≈ 3.7798
| N | ∛N |
|---|---|
| 1 | 1 |
| 8 | 2 |
| 27 | 3 |
| 64 | 4 |
| 125 | 5 |
| 216 | 6 |
| 343 | 7 |
| 512 | 8 |
| 729 | 9 |
| 1,000 | 10 |
| 1,331 | 11 |
| 1,728 | 12 |
| 2,197 | 13 |
| 2,744 | 14 |
| 3,375 | 15 |
| 4,096 | 16 |
| 4,913 | 17 |
| 5,832 | 18 |
| 6,859 | 19 |
| 8,000 | 20 |
| x | ∛x |
|---|---|
| 0.001 | 0.1 |
| 0.008 | 0.2 |
| 0.027 | 0.3 |
| 0.064 | 0.4 |
| 0.125 | 0.5 |
| 1/8 | 1/2 = 0.5 |
| 1/27 | 1/3 ≈ 0.3333 |
| 8/27 | 2/3 ≈ 0.6667 |
| 64/125 | 4/5 = 0.8 |
Common mistakes
- A cube root is not division by 3: ∛27 = 3, while 27 ÷ 3 = 9.
- A negative number has a cube root (∛(−8) = −2), but Excel gives #NUM! for =(-8)^(1/3), and many calculators give an error for (−8)^(1/3). Take the root of the absolute value and put the minus in front: =-(8^(1/3)) gives −2.
- The cube root is not the cube: ∛8 = 2, while 8³ = 512.
See Also
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Prime Factorization - Prime Factorization Calculator
- Scientific Calculator with Memory & History - Free Engineering Calculator Online with Memory Function, Operation History, Logarithms & Trigonometry. Similar to ti-83, ti-84, ti-89
Last Results
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Cube Root of 1.2 (∛1.2): Exact Value and Decimal
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Cube Root of 1323 (∛1323): Exact Value and Decimal
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Cube Root of 0.025 (∛0.025): Exact Value and Decimal
Cube Root of 0.512 (∛0.512): Exact Value and Decimal
Cube Root of 12 (∛12): Exact Value and Decimal
Cube Root of 10000 (∛10000): Exact Value and Decimal
Cube Root of 1125 (∛1125): Exact Value and Decimal
Cube Root of 1 (∛1): Exact Value and Decimal
Cube Root of −108 (∛(−108)): Exact Value and Decimal
Cube Root of −54 (∛(−54)): Exact Value and Decimal
Cube Root of −21 (∛(−21)): Exact Value and Decimal
Cube Root of 17576 (∛17576): Exact Value and Decimal
Cube Root of 1700 (∛1700): Exact Value and Decimal
Cube Root of 162 (∛162): Exact Value and Decimal
Cube Root of 1725 (∛1725): Exact Value and Decimal
Cube Root of 140608 (∛140608): Exact Value and Decimal
Cube Root of 1024 (∛1024): Exact Value and Decimal
Cube Root of 149 (∛149): Exact Value and Decimal
Cube Root of −15 (∛(−15)): Exact Value and Decimal
Cube Root of 0.064 (∛0.064): Exact Value and Decimal
Cube Root of 13824 (∛13824): Exact Value and Decimal
Cube Root of 158 (∛158): Exact Value and Decimal
Cube Root of 12.167 (∛12.167): Exact Value and Decimal
Cube Root of 1331 (∛1331): Exact Value and Decimal
Cube Root of 121 (∛121): Exact Value and Decimal
Cube Root of 1729 (∛1729): Exact Value and Decimal
Cube Root of 0 (∛0): Exact Value and Decimal
Cube Root of 0.1 (∛0.1): Exact Value and Decimal
Cube Root of 1/4 (∛(1/4)): Exact Value and Decimal
Cube Root of 1/343 (∛(1/343)): Exact Value and Decimal
Cube Root of 11 (∛11): Exact Value and Decimal
Cube Root of 136 (∛136): Exact Value and Decimal
Cube Root of −6859 (∛(−6859)): Exact Value and Decimal
Cube Root of 127 (∛127): Exact Value and Decimal
Cube Root of −7 (∛(−7)): Exact Value and Decimal
Cube Root of 173 (∛173): Exact Value and Decimal
Cube Root of −729 (∛(−729)): Exact Value and Decimal
Cube Root of 166375 (∛166375): Exact Value and Decimal
Cube Root of 15625 (∛15625): Exact Value and Decimal
Cube Root of 0.04 (∛0.04): Exact Value and Decimal
Cube Root of 11025 (∛11025): Exact Value and Decimal
Cube Root of 126 (∛126): Exact Value and Decimal
Cube Root of 1/25 (∛(1/25)): Exact Value and Decimal
Cube Root of −125 (∛(−125)): Exact Value and Decimal
Cube Root of −0.0125 (∛(−0.0125)): Exact Value and Decimal
Cube Root of 12167 (∛12167): Exact Value and Decimal
Cube Root of 1210 (∛1210): Exact Value and Decimal
Cube Root of 125/512 (∛(125/512)): Exact Value and Decimal
Cube Root of 131 (∛131): Exact Value and Decimal
Cube Root of 0.08 (∛0.08): Exact Value and Decimal