What is the cube root of 6?

The cube root of 6 is cbrt6. In decimal: cbrt(6) approximately 1.8171205928 This is irrational. cbrt(6) approx 1.81712 is irrational. 6 = 2 x 3 has no perfect cube factors.

No. 6 is not a perfect cube. 1^3 = 1 and 2^3 = 8. Since 6 falls between these, cbrt(6) is not an integer. Nearest perfect cubes: 1 (= 1^3) and 8 (= 2^3).

What is cbrt(6) cubed?

(cbrt(6))^3 = 6. This follows from the definition: cbrt(n) is the number that when cubed gives n. So (cbrt(6))^3 = 6 always.

How is cube root different from square root?

Square root: sqrt(6) approximately 2.449490. Cube root: cbrt(6) approximately 1.817121. 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). 6 is not a perfect cube. The next perfect cube after 27 is 64 (= 4^3).

Cube Root of 6 — cbrt(6) = cbrt6

The cube root of 6 is cbrt6. In decimal, cbrt(6) is approximately 1.817121 (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....

∛6 = ?

CUBE ROOT OF 6

∛6

≈ 1.8171205928

Irrational — decimal never ends or repeats

Exact form

∛6

Decimal (6dp)

1.817121

Decimal (10dp)

1.8171205928

Is perfect cube?

(∛6)³

6 ✓

Between

1 and 2

DECIMAL PRECISION

∛6 ≈ 1.8171205928

STEP-BY-STEP

Prime factorisation: 6 = 2 × 3

No perfect cube factor — ∛6 is already in simplest form

1³ = 1 < 6 < 8 = 2³ → ∛6 between 1 and 2

∛6 ≈ 1.8171205928

FUN FACT

cbrt(6) approx 1.81712 is irrational. 6 = 2 x 3 has no perfect cube factors.

NUMBER LINE (∛6 ≈ 1.8171)

∛6

CUBE WITH VOLUME = 6

NEARBY PERFECT CUBES

∛0= 00³ = 0

∛1= 11³ = 1

∛8= 22³ = 8

∛27= 33³ = 27

∛64= 44³ = 64

CUBE ROOT LAWS

∛6 × ∛6 × ∛6= 6

(∛6)³= 6

∛(6 × 8)= 2∛6 ≈ 3.6342

∛(6 / 8)= ∛6/2 ≈ 0.9086

∛6 × ∛7≈ 3.4760

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HOW TO CALCULATE

1
Find the prime factorisation of 6: 6 = 2 x 3. Look for any prime appearing 3+ times.
2
No factor appears 3+ times, so cbrt(6) cannot be simplified and stays as cbrt(6).
3
Locate cbrt(6) between integers: 1^3 = 1 < 6 < 8 = 2^3. So cbrt(6) is between 1 and 2.
4
Decimal: cbrt(6) approximately 1.8171205928. Verify: (1.817121)^3 approximately 6.

WORKED EXAMPLE

cbrt(6): not a perfect cube. Factorisation: 6 = 2 x 3. Simplified: cbrt6. Decimal: cbrt(6) approximately 1.8171205928.

FREQUENTLY ASKED QUESTIONS

OTHER CUBE ROOTS

∛1 ∛2 ∛3 ∛4 ∛5 ∛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.