Cube root of 12
∛12 = 2.289 to three decimal places; it cannot be simplified.
∛12 = 2.289
12 is not a perfect cube, so its cube root is irrational. To three decimal places ∛12 = 2.289.
12 has no cube factor bigger than 1, so ∛12 cannot be simplified.
Method 1: prime factorisation, in threes
12 = 22 × 3.
Group in threes where you can: 1³ × 12, so ∛12 = 1∛12.
Method 2: estimate between two cubes
2³ = 8 and 3³ = 27, so ∛12 is between 2 and 3. A refinement: x = 2 + (12 − 8) ÷ (27 − 8) ≈ 2.21, against the true 2.289.
The cubes worth memorising
| n | n³ |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1,000 |
| 11 | 1,331 |
| 12 | 1,728 |
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find ∛27.
Answer: 3
2. Between which two whole numbers is ∛17?
Answer: 2 and 3
3. Simplify ∛96.
Answer: 2∛12
4. Is 13 a perfect cube?
Answer: no
5. What is (∛12)³?
Answer: 12
📚 The class this belongs to
Cube roots are taught in Grade 8 in the US (Common Core 8.EE.2), Year 8 and 9 in the UK, Class 8 in CBSE (NCERT Class 8, Cubes and Cube Roots) and Year 8 in Australia.
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