Cube Root of 24 — Value and Simplification Steps

Q: What is the cube root of 24 in simplest radical form?

It is $2\sqrt[3]{3}$, found by pulling the perfect-cube factor $2^3 = 8$ out of 24.

Q: Is the cube root of 24 rational or irrational?

Irrational. Since 24 is not a perfect cube, $\sqrt[3]{24}$ is a non-terminating, non-repeating decimal, about $2.884$.

Q: What is the cube root of 24 as a decimal?

Approximately $2.884$ to three decimal places.

Q: Why does 2 come out of $\sqrt[3]{24}$ but 3 does not?

Because $24 = 2^3 \times 3$. The factor $2^3$ is a perfect cube, so its cube root is the whole number 2; the lone 3 has no cube factor, so it remains under the radical.

Q: How is the cube root of 24 different from the cube root of 27?

$\sqrt[3]{27} = 3$ exactly, because 27 is a perfect cube. $\sqrt[3]{24}$ is irrational and simplifies only to $2\sqrt[3]{3}$.

The cube root of 24 is not a whole number, but it does simplify neatly to $2\sqrt[3]{3}$ .

Quick Answer:
Result: $\sqrt[3]{24} = 2\sqrt[3]{3} \approx 2.884$
Notation: $\sqrt[3]{24}$ or $24^{1/3}$
Method shown: prime factorization
Approximate value: $2.884$ (to 3 decimal places, irrational)
Exact form: $2\sqrt[3]{3}$

Quick Reference Table

Number	Simplified cube root	Decimal (3 dp)
$\sqrt[3]{8}$	$2$	$2.000$
$\sqrt[3]{16}$	$2\sqrt[3]{2}$	$2.520$
$\sqrt[3]{24}$	$2\sqrt[3]{3}$	$2.884$
$\sqrt[3]{27}$	$3$	$3.000$
$\sqrt[3]{54}$	$3\sqrt[3]{2}$	$3.780$
$\sqrt[3]{64}$	$4$	$4.000$

Where the Cube Root of 24 Appears

The cube root of 24 turns up whenever a volume is known and an edge length is wanted. If a cube-shaped tank holds 24 cubic units, each edge measures $\sqrt[3]{24} \approx 2.884$ units. The same simplification pattern — pulling a perfect-cube factor out from under the radical — is exactly what scientific and engineering calculators do internally before rounding.

What Is the Cube Root of 24?

The cube root of a number is the value that, multiplied by itself three times, returns that number. Since 24 is not a perfect cube — it sits between $2^3 = 8$ and $3^3 = 27$ — its cube root is an irrational number that never terminates.

But it is not fully "stuck" under the radical. Because 24 contains the perfect-cube factor 8, part of it can come out, leaving the simplified form $2\sqrt[3]{3}$ . This is the same skill used across cube numbers and radicals.

How to Simplify the Cube Root of 24 (Methods)

Method 1: Prime factorization

Break 24 into its prime factors.

$24 = 2 \times 2 \times 2 \times 3$ $24 = 2^3 \times 3$

Write the cube root over the factored form.

$\sqrt[3]{24} = \sqrt[3]{2^3 \times 3}$

The cube root of $2^3$ is 2, so 2 comes out of the radical while the 3 stays inside.

$\sqrt[3]{24} = 2\sqrt[3]{3}$

Final answer: $\sqrt[3]{24} = 2\sqrt[3]{3}$ .

Method 2: Estimation for the decimal value

Locate 24 between neighbouring perfect cubes.

$2^3 = 8$ $3^3 = 27$

So $\sqrt[3]{24}$ lies between 2 and 3, and close to 3 because 24 is close to 27. Testing $2.9$ :

$2.9^3 = 24.389$

That is slightly above 24, so the answer is a touch below 2.9. Testing $2.88$ :

$2.88^3 \approx 23.888$

Final answer: $\sqrt[3]{24} \approx 2.884$ to three decimal places.

Common Mistakes With Cube Root of 24

Mistake 1: Dropping the cube-root index

Where it slips in: writing the radical quickly.

Don't do this: writing $\sqrt{24}$ when you mean the cube root.

The correct way: always show the index: $\sqrt[3]{24}$ . Without the little 3 it reads as a square root, giving $\approx 4.899$ instead of $\approx 2.884$ .

Mistake 2: Pulling out the wrong factor

Where it slips in: simplifying by removing any factor instead of a perfect-cube factor.

Don't do this: writing $\sqrt[3]{24} = 4\sqrt[3]{6}$ by splitting off 4.

The correct way: only a perfect cube factor can leave the radical. Here that is $2^3 = 8$ , giving $2\sqrt[3]{3}$ .

Mistake 3: Treating the cube root like a square root when simplifying

Where it slips in: grouping factors in pairs instead of triples.

Don't do this: taking one factor out for every pair of 2's.

The correct way: a cube root removes a factor for every three copies. Three 2's give one 2 outside; the leftover 3 has no triple, so it stays inside.

To build cube-root fluency with a teacher, explore Bhanzu's algebra tutor or math classes online.

Was this article helpful?

Your feedback helps us write better content

Frequently Asked Questions

What is the cube root of 24 in simplest radical form?

It is

2\sqrt[3]{3}

, found by pulling the perfect-cube factor

2^3 = 8

out of 24.

Is the cube root of 24 rational or irrational?

Irrational. Since 24 is not a perfect cube,

\sqrt[3]{24}

is a non-terminating, non-repeating decimal, about

2.884

What is the cube root of 24 as a decimal?

Approximately

2.884

to three decimal places.

Why does 2 come out of

\sqrt[3]{24}

but 3 does not?

Because

24 = 2^3 \times 3

. The factor

2^3

is a perfect cube, so its cube root is the whole number 2; the lone 3 has no cube factor, so it remains under the radical.

How is the cube root of 24 different from the cube root of 27?

\sqrt[3]{27} = 3

exactly, because 27 is a perfect cube.

\sqrt[3]{24}

is irrational and simplifies only to

2\sqrt[3]{3}

✍️ Written By

Bhanzu Team

Content Creator and Editor

Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.