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Cube Root of 24

The value of the cube root of 24 rounded to 6 decimal places is 2.884499. It is the real solution of the equation x³ = 24. The cube root of 24 is expressed as ∛24 or 2 ∛3 in the radical form and as (24)^⅓ or (24)^0.33 in the exponent form. The prime factorization of 24 is 2 × 2 × 2 × 3, hence, the cube root of 24 in its lowest radical form is expressed as 2 ∛3.

Cube root of 24: 2.884499141
Cube root of 24 in Exponential Form: (24)^⅓
Cube root of 24 in Radical Form: ∛24 or 2 ∛3

Cube Root of 24

1.	What is the Cube Root of 24?
2.	How to Calculate the Cube Root of 24?
3.	Is the Cube Root of 24 Irrational?
4.	FAQs on Cube Root of 24

What is the Cube Root of 24?

The cube root of 24 is the number which when multiplied by itself three times gives the product as 24. Since 24 can be expressed as 2 × 2 × 2 × 3. Therefore, the cube root of 24 = ∛(2 × 2 × 2 × 3) = 2.8845.

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How to Calculate the Value of the Cube Root of 24?

Cube Root of 24 by Halley's Method

Its formula is ∛a ≈ x ((x³ + 2a)/(2x³ + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.

Here a = 24
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 24]
⇒ x = 2
Therefore,
∛24 = 2 (2³ + 2 × 24)/(2 × 2³ + 24)) = 2.8
⇒ ∛24 ≈ 2.8
Therefore, the cube root of 24 is 2.8 approximately.

Is the Cube Root of 24 Irrational?

Yes, because ∛24 = ∛(2 × 2 × 2 × 3) = 2 ∛3 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 24 is an irrational number.

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Cube Root of 24 Solved Examples

Example 1: The volume of a spherical ball is 24π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 24π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 24
⇒ R = ∛(3/4 × 24) = ∛(3/4) × ∛24 = 0.90856 × 2.8845 (∵ ∛(3/4) = 0.90856 and ∛24 = 2.8845)
⇒ R = 2.62074 in³
Example 2: Given the volume of a cube is 24 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 24 in³ = a³
⇒ a³ = 24
Cube rooting on both sides,
⇒ a = ∛24 in
Since the cube root of 24 is 2.88, therefore, the length of the side of the cube is 2.88 in.
Example 3: Find the real root of the equation x³ − 24 = 0.

Solution:

x³ − 24 = 0 i.e. x³ = 24
Solving for x gives us,
x = ∛24, x = ∛24 × (-1 + √3i))/2 and x = ∛24 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛24
Therefore, the real root of the equation x³ − 24 = 0 is for x = ∛24 = 2.8845.

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FAQs on Cube Root of 24

What is the Value of the Cube Root of 24?

We can express 24 as 2 × 2 × 2 × 3 i.e. ∛24 = ∛(2 × 2 × 2 × 3) = 2.8845. Therefore, the value of the cube root of 24 is 2.8845.

Why is the Value of the Cube Root of 24 Irrational?

The value of the cube root of 24 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛24 is irrational.

Is 24 a Perfect Cube?

The number 24 on prime factorization gives 2 × 2 × 2 × 3. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 24 is irrational, hence 24 is not a perfect cube.

How to Simplify the Cube Root of 24/512?

We know that the cube root of 24 is 2.8845 and the cube root of 512 is 8. Therefore, ∛(24/512) = (∛24)/(∛512) = 2.884/8 = 0.3605.

What is the Value of 3 Plus 19 Cube Root 24?

The value of ∛24 is 2.884. So, 3 + 19 × ∛24 = 3 + 19 × 2.884 = 57.796. Hence, the value of 3 plus 19 cube root 24 is 57.796.

If the Cube Root of 24 is 2.88, Find the Value of ∛0.024.

Let us represent ∛0.024 in p/q form i.e. ∛(24/1000) = 2.88/10 = 0.29. Hence, the value of ∛0.024 = 0.29.

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