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Cube Root of 96

The value of the cube root of 96 rounded to 4 decimal places is 4.5789. It is the real solution of the equation x³ = 96. The cube root of 96 is expressed as ∛96 or 2 ∛12 in the radical form and as (96)^⅓ or (96)^0.33 in the exponent form. The prime factorization of 96 is 2 × 2 × 2 × 2 × 2 × 3, hence, the cube root of 96 in its lowest radical form is expressed as 2 ∛12.

Cube root of 96: 4.57885697
Cube root of 96 in Exponential Form: (96)^⅓
Cube root of 96 in Radical Form: ∛96 or 2 ∛12

Cube Root of 96

1.	What is the Cube Root of 96?
2.	How to Calculate the Cube Root of 96?
3.	Is the Cube Root of 96 Irrational?
4.	FAQs on Cube Root of 96

What is the Cube Root of 96?

The cube root of 96 is the number which when multiplied by itself three times gives the product as 96. Since 96 can be expressed as 2 × 2 × 2 × 2 × 2 × 3. Therefore, the cube root of 96 = ∛(2 × 2 × 2 × 2 × 2 × 3) = 4.5789.

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How to Calculate the Value of the Cube Root of 96?

Cube Root of 96 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 = 96
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 96]
⇒ x = 4
Therefore,
∛96 = 4 (4³ + 2 × 96)/(2 × 4³ + 96)) = 4.57
⇒ ∛96 ≈ 4.57
Therefore, the cube root of 96 is 4.57 approximately.

Is the Cube Root of 96 Irrational?

Yes, because ∛96 = ∛(2 × 2 × 2 × 2 × 2 × 3) = 2 ∛12 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 96 is an irrational number.

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Cube Root of 96 Solved Examples

Example 1: What is the value of ∛96 ÷ ∛(-96)?

Solution:

The cube root of -96 is equal to the negative of the cube root of 96.
⇒ ∛-96 = -∛96

Therefore,
⇒ ∛96/∛(-96) = ∛96/(-∛96) = -1
Example 2: Find the real root of the equation x³ − 96 = 0.

Solution:

x³ − 96 = 0 i.e. x³ = 96
Solving for x gives us,
x = ∛96, x = ∛96 × (-1 + √3i))/2 and x = ∛96 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛96
Therefore, the real root of the equation x³ − 96 = 0 is for x = ∛96 = 4.5789.
Example 3: The volume of a spherical ball is 96π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 96π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 96
⇒ R = ∛(3/4 × 96) = ∛(3/4) × ∛96 = 0.90856 × 4.57886 (∵ ∛(3/4) = 0.90856 and ∛96 = 4.57886)
⇒ R = 4.16017 in³

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FAQs on Cube Root of 96

What is the Value of the Cube Root of 96?

We can express 96 as 2 × 2 × 2 × 2 × 2 × 3 i.e. ∛96 = ∛(2 × 2 × 2 × 2 × 2 × 3) = 4.57886. Therefore, the value of the cube root of 96 is 4.57886.

If the Cube Root of 96 is 4.58, Find the Value of ∛0.096.

Let us represent ∛0.096 in p/q form i.e. ∛(96/1000) = 4.58/10 = 0.46. Hence, the value of ∛0.096 = 0.46.

What is the Cube Root of -96?

The cube root of -96 is equal to the negative of the cube root of 96. Therefore, ∛-96 = -(∛96) = -(4.579) = -4.579.

Why is the Value of the Cube Root of 96 Irrational?

The value of the cube root of 96 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛96 is irrational.

What is the Cube of the Cube Root of 96?

The cube of the cube root of 96 is the number 96 itself i.e. (∛96)³ = (96^1/3)³ = 96.

Is 96 a Perfect Cube?

The number 96 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 96 is irrational, hence 96 is not a perfect cube.

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