What is the cube root of 7?

The cube root of 7 is cbrt7. In decimal: cbrt(7) approximately 1.9129311828 This is irrational. cbrt(7) approx 1.91293 is irrational. 7 is prime.

No. 7 is not a perfect cube. 1^3 = 1 and 2^3 = 8. Since 7 falls between these, cbrt(7) is not an integer. Nearest perfect cubes: 1 (= 1^3) and 8 (= 2^3).

What is cbrt(7) cubed?

(cbrt(7))^3 = 7. This follows from the definition: cbrt(n) is the number that when cubed gives n. So (cbrt(7))^3 = 7 always.

How is cube root different from square root?

Square root: sqrt(7) approximately 2.645751. Cube root: cbrt(7) approximately 1.912931. 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). 7 is not a perfect cube. The next perfect cube after 27 is 64 (= 4^3).

Cube Root of 7 — cbrt(7) = cbrt7

The cube root of 7 is cbrt7. In decimal, cbrt(7) is approximately 1.912931 (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....

∛7 = ?

CUBE ROOT OF 7

∛7

≈ 1.9129311828

Irrational — decimal never ends or repeats

Exact form

∛7

Decimal (6dp)

1.912931

Decimal (10dp)

1.9129311828

Is perfect cube?

(∛7)³

7 ✓

Between

1 and 2

DECIMAL PRECISION

∛7 ≈ 1.9129311828

STEP-BY-STEP

Prime factorisation: 7 = 7

No perfect cube factor — ∛7 is already in simplest form

1³ = 1 < 7 < 8 = 2³ → ∛7 between 1 and 2

∛7 ≈ 1.9129311828

FUN FACT

cbrt(7) approx 1.91293 is irrational. 7 is prime.

NUMBER LINE (∛7 ≈ 1.9129)

∛7

CUBE WITH VOLUME = 7

NEARBY PERFECT CUBES

∛0= 00³ = 0

∛1= 11³ = 1

∛8= 22³ = 8

∛27= 33³ = 27

∛64= 44³ = 64

CUBE ROOT LAWS

∛7 × ∛7 × ∛7= 7

(∛7)³= 7

∛(7 × 8)= 2∛7 ≈ 3.8259

∛(7 / 8)= ∛7/2 ≈ 0.9565

∛7 × ∛8≈ 3.8259

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HOW TO CALCULATE

1
Find the prime factorisation of 7: 7 = 7. Look for any prime appearing 3+ times.
2
No factor appears 3+ times, so cbrt(7) cannot be simplified and stays as cbrt(7).
3
Locate cbrt(7) between integers: 1^3 = 1 < 7 < 8 = 2^3. So cbrt(7) is between 1 and 2.
4
Decimal: cbrt(7) approximately 1.9129311828. Verify: (1.912931)^3 approximately 7.

WORKED EXAMPLE

cbrt(7): not a perfect cube. Factorisation: 7 = 7. Simplified: cbrt7. Decimal: cbrt(7) approximately 1.9129311828.

FREQUENTLY ASKED QUESTIONS

OTHER CUBE ROOTS

∛1 ∛2 ∛3 ∛4 ∛5 ∛6 ∛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.