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.
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