What is the cube root of 3?

The cube root of 3 is cbrt3. In decimal: cbrt(3) approximately 1.4422495703 This is irrational. cbrt(3) approx 1.44225 is irrational. 3 is prime so cbrt(3) cannot be simplified.

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

What is cbrt(3) cubed?

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

How is cube root different from square root?

Square root: sqrt(3) approximately 1.732051. Cube root: cbrt(3) approximately 1.442250. 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). 3 is not a perfect cube. The next perfect cube after 27 is 64 (= 4^3).

Cube Root of 3 — cbrt(3) = cbrt3

The cube root of 3 is cbrt3. In decimal, cbrt(3) is approximately 1.44225 (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....

∛3 = ?

CUBE ROOT OF 3

∛3

≈ 1.4422495703

Irrational — decimal never ends or repeats

Exact form

∛3

Decimal (6dp)

1.442250

Decimal (10dp)

1.4422495703

Is perfect cube?

(∛3)³

3 ✓

Between

1 and 2

DECIMAL PRECISION

∛3 ≈ 1.4422495703

STEP-BY-STEP

Prime factorisation: 3 = 3

No perfect cube factor — ∛3 is already in simplest form

1³ = 1 < 3 < 8 = 2³ → ∛3 between 1 and 2

∛3 ≈ 1.4422495703

FUN FACT

cbrt(3) approx 1.44225 is irrational. 3 is prime so cbrt(3) cannot be simplified.

NUMBER LINE (∛3 ≈ 1.4422)

∛3

CUBE WITH VOLUME = 3

NEARBY PERFECT CUBES

∛0= 00³ = 0

∛1= 11³ = 1

∛8= 22³ = 8

∛27= 33³ = 27

∛64= 44³ = 64

CUBE ROOT LAWS

∛3 × ∛3 × ∛3= 3

(∛3)³= 3

∛(3 × 8)= 2∛3 ≈ 2.8845

∛(3 / 8)= ∛3/2 ≈ 0.7211

∛3 × ∛4≈ 2.2894

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HOW TO CALCULATE

1
Find the prime factorisation of 3: 3 = 3. Look for any prime appearing 3+ times.
2
No factor appears 3+ times, so cbrt(3) cannot be simplified and stays as cbrt(3).
3
Locate cbrt(3) between integers: 1^3 = 1 < 3 < 8 = 2^3. So cbrt(3) is between 1 and 2.
4
Decimal: cbrt(3) approximately 1.4422495703. Verify: (1.44225)^3 approximately 3.

WORKED EXAMPLE

cbrt(3): not a perfect cube. Factorisation: 3 = 3. Simplified: cbrt3. Decimal: cbrt(3) approximately 1.4422495703.

FREQUENTLY ASKED QUESTIONS

OTHER CUBE ROOTS

∛1 ∛2 ∛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.