What is the cube root of 13?

The cube root of 13 is cbrt13. In decimal: cbrt(13) approximately 2.3513346877 This is irrational. cbrt(13) approx 2.35133 is irrational. 13 is prime.

Is 13 a perfect cube?

No. 13 is not a perfect cube. 2^3 = 8 and 3^3 = 27. Since 13 falls between these, cbrt(13) is not an integer. Nearest perfect cubes: 8 (= 2^3) and 27 (= 3^3).

What is cbrt(13) cubed?

(cbrt(13))^3 = 13. This follows from the definition: cbrt(n) is the number that when cubed gives n. So (cbrt(13))^3 = 13 always.

How is cube root different from square root?

Square root: sqrt(13) approximately 3.605551. Cube root: cbrt(13) approximately 2.351335. 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). 13 is not a perfect cube. The next perfect cube after 27 is 64 (= 4^3).

Cube Root of 13 — cbrt(13) = cbrt13

The cube root of 13 is cbrt13. In decimal, cbrt(13) is approximately 2.351335 (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....

∛13 = ?

CUBE ROOT OF 13

∛13

≈ 2.3513346877

Irrational — decimal never ends or repeats

Exact form

∛13

Decimal (6dp)

2.351335

Decimal (10dp)

2.3513346877

Is perfect cube?

(∛13)³

13 ✓

Between

2 and 3

DECIMAL PRECISION

∛13 ≈ 2.3513346877

STEP-BY-STEP

Prime factorisation: 13 = 13

No perfect cube factor — ∛13 is already in simplest form

2³ = 8 < 13 < 27 = 3³ → ∛13 between 2 and 3

∛13 ≈ 2.3513346877

FUN FACT

cbrt(13) approx 2.35133 is irrational. 13 is prime.

NUMBER LINE (∛13 ≈ 2.3513)

∛13

CUBE WITH VOLUME = 13

NEARBY PERFECT CUBES

∛1= 11³ = 1

∛8= 22³ = 8

∛27= 33³ = 27

∛64= 44³ = 64

∛125= 55³ = 125

CUBE ROOT LAWS

∛13 × ∛13 × ∛13= 13

(∛13)³= 13

∛(13 × 8)= 2∛13 ≈ 4.7027

∛(13 / 8)= ∛13/2 ≈ 1.1757

∛13 × ∛14≈ 5.6671

Created with❤️byeaglecalculator.com

HOW TO CALCULATE

1
Find the prime factorisation of 13: 13 = 13. Look for any prime appearing 3+ times.
2
No factor appears 3+ times, so cbrt(13) cannot be simplified and stays as cbrt(13).
3
Locate cbrt(13) between integers: 2^3 = 8 < 13 < 27 = 3^3. So cbrt(13) is between 2 and 3.
4
Decimal: cbrt(13) approximately 2.3513346877. Verify: (2.351335)^3 approximately 13.

WORKED EXAMPLE

cbrt(13): not a perfect cube. Factorisation: 13 = 13. Simplified: cbrt13. Decimal: cbrt(13) approximately 2.3513346877.

FREQUENTLY ASKED QUESTIONS

OTHER CUBE ROOTS

∛1 ∛2 ∛3 ∛4 ∛5 ∛6 ∛7 ∛8 ∛9 ∛10 ∛11 ∛12 ∛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.