What is the cube root of 21?

The cube root of 21 is cbrt21. In decimal: cbrt(21) approximately 2.7589241764 This is irrational. cbrt(21) approx 2.75892 is irrational. 21 = 3 x 7, no perfect cube factors.

Is 21 a perfect cube?

No. 21 is not a perfect cube. 2^3 = 8 and 3^3 = 27. Since 21 falls between these, cbrt(21) is not an integer. Nearest perfect cubes: 8 (= 2^3) and 27 (= 3^3).

What is cbrt(21) cubed?

(cbrt(21))^3 = 21. This follows from the definition: cbrt(n) is the number that when cubed gives n. So (cbrt(21))^3 = 21 always.

How is cube root different from square root?

Square root: sqrt(21) approximately 4.582576. Cube root: cbrt(21) approximately 2.758924. 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). 21 is not a perfect cube. The next perfect cube after 27 is 64 (= 4^3).

Cube Root of 21 — cbrt(21) = cbrt21

The cube root of 21 is cbrt21. In decimal, cbrt(21) is approximately 2.758924 (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....

∛21 = ?

CUBE ROOT OF 21

∛21

≈ 2.7589241764

Irrational — decimal never ends or repeats

Exact form

∛21

Decimal (6dp)

2.758924

Decimal (10dp)

2.7589241764

Is perfect cube?

(∛21)³

21 ✓

Between

2 and 3

DECIMAL PRECISION

∛21 ≈ 2.7589241764

STEP-BY-STEP

Prime factorisation: 21 = 3 × 7

No perfect cube factor — ∛21 is already in simplest form

2³ = 8 < 21 < 27 = 3³ → ∛21 between 2 and 3

∛21 ≈ 2.7589241764

FUN FACT

cbrt(21) approx 2.75892 is irrational. 21 = 3 x 7, no perfect cube factors.

NUMBER LINE (∛21 ≈ 2.7589)

∛21

CUBE WITH VOLUME = 21

NEARBY PERFECT CUBES

∛1= 11³ = 1

∛8= 22³ = 8

∛27= 33³ = 27

∛64= 44³ = 64

∛125= 55³ = 125

CUBE ROOT LAWS

∛21 × ∛21 × ∛21= 21

(∛21)³= 21

∛(21 × 8)= 2∛21 ≈ 5.5178

∛(21 / 8)= ∛21/2 ≈ 1.3795

∛21 × ∛22≈ 7.7306

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HOW TO CALCULATE

1
Find the prime factorisation of 21: 21 = 3 x 7. Look for any prime appearing 3+ times.
2
No factor appears 3+ times, so cbrt(21) cannot be simplified and stays as cbrt(21).
3
Locate cbrt(21) between integers: 2^3 = 8 < 21 < 27 = 3^3. So cbrt(21) is between 2 and 3.
4
Decimal: cbrt(21) approximately 2.7589241764. Verify: (2.758924)^3 approximately 21.

WORKED EXAMPLE

cbrt(21): not a perfect cube. Factorisation: 21 = 3 x 7. Simplified: cbrt21. Decimal: cbrt(21) approximately 2.7589241764.

FREQUENTLY ASKED QUESTIONS

OTHER CUBE ROOTS

∛1 ∛2 ∛3 ∛4 ∛5 ∛6 ∛7 ∛8 ∛9 ∛10 ∛11 ∛12 ∛13 ∛14 ∛15 ∛16 ∛17 ∛18 ∛19 ∛20 ∛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.