What is the cube root of 2?

The cube root of 2 is cbrt2. In decimal: cbrt(2) approximately 1.2599210499 This is irrational. cbrt(2) approx 1.25992 is irrational. It appears in the ancient 'doubling the cube' problem — impossible with compass and straightedge alone.

No. 2 is not a perfect cube. 1^3 = 1 and 2^3 = 8. Since 2 falls between these, cbrt(2) is not an integer. Nearest perfect cubes: 1 (= 1^3) and 8 (= 2^3).

What is cbrt(2) cubed?

(cbrt(2))^3 = 2. This follows from the definition: cbrt(n) is the number that when cubed gives n. So (cbrt(2))^3 = 2 always.

How is cube root different from square root?

Square root: sqrt(2) approximately 1.414214. Cube root: cbrt(2) approximately 1.259921. Key differences: - Cube roots exist for negative numbers: cbrt(-8) = -2. Square roots of negatives are imaginary. - Cube roots grow more slowly than square roots. - Perfect cubes are rarer than perfect squares.

What are the perfect cubes from 1 to 30?

Only three: 1 (= 1^3), 8 (= 2^3), and 27 (= 3^3). 2 is not a perfect cube. The next perfect cube after 27 is 64 (= 4^3).

Cube Root of 2 — cbrt(2) = cbrt2

The cube root of 2 is cbrt2. In decimal, cbrt(2) is approximately 1.259921 (irrational — the decimal never ends or repeats). This page shows the exact value, simplified radical form, decimal to 20 decimal places, step-by-step working, and a 3D cube visualisation....

∛2 = ?

CUBE ROOT OF 2

∛2

≈ 1.2599210499

Irrational — decimal never ends or repeats

Exact form

∛2

Decimal (6dp)

1.259921

Decimal (10dp)

1.2599210499

Is perfect cube?

(∛2)³

2 ✓

Between

1 and 2

DECIMAL PRECISION

∛2 ≈ 1.2599210499

STEP-BY-STEP

Prime factorisation: 2 = 2

No perfect cube factor — ∛2 is already in simplest form

1³ = 1 < 2 < 8 = 2³ → ∛2 between 1 and 2

∛2 ≈ 1.2599210499

FUN FACT

cbrt(2) approx 1.25992 is irrational. It appears in the ancient 'doubling the cube' problem — impossible with compass and straightedge alone.

NUMBER LINE (∛2 ≈ 1.2599)

∛2

CUBE WITH VOLUME = 2

NEARBY PERFECT CUBES

∛0= 00³ = 0

∛1= 11³ = 1

∛8= 22³ = 8

∛27= 33³ = 27

∛64= 44³ = 64

CUBE ROOT LAWS

∛2 × ∛2 × ∛2= 2

(∛2)³= 2

∛(2 × 8)= 2∛2 ≈ 2.5198

∛(2 / 8)= ∛2/2 ≈ 0.6300

∛2 × ∛3≈ 1.8171

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HOW TO CALCULATE

1
Find the prime factorisation of 2: 2 = 2. Look for any prime appearing 3+ times.
2
No factor appears 3+ times, so cbrt(2) cannot be simplified and stays as cbrt(2).
3
Locate cbrt(2) between integers: 1^3 = 1 < 2 < 8 = 2^3. So cbrt(2) is between 1 and 2.
4
Decimal: cbrt(2) approximately 1.2599210499. Verify: (1.259921)^3 approximately 2.

WORKED EXAMPLE

cbrt(2): not a perfect cube. Factorisation: 2 = 2. Simplified: cbrt2. Decimal: cbrt(2) approximately 1.2599210499.

FREQUENTLY ASKED QUESTIONS

OTHER CUBE ROOTS

∛1 ∛3 ∛4 ∛5 ∛6 ∛7 ∛8 ∛9 ∛10 ∛11 ∛12 ∛13 ∛14 ∛15 ∛16 ∛17 ∛18 ∛19 ∛20 ∛21 ∛22 ∛23 ∛24 ∛25 ∛26 ∛27 ∛28 ∛29 ∛30

Bold bordered = perfect cubes (∛1=1, ∛8=2, ∛27=3)

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Last updated: April 28, 2026 · Verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.