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Cube Root of 144

The value of the cube root of 144 rounded to 5 decimal places is 5.24148. It is the real solution of the equation x³ = 144. The cube root of 144 is expressed as ∛144 or 2 ∛18 in the radical form and as (144)^⅓ or (144)^0.33 in the exponent form. The prime factorization of 144 is 2 × 2 × 2 × 2 × 3 × 3, hence, the cube root of 144 in its lowest radical form is expressed as 2 ∛18.

Cube root of 144: 5.241482788
Cube root of 144 in Exponential Form: (144)^⅓
Cube root of 144 in Radical Form: ∛144 or 2 ∛18

Cube Root of 144

1.	What is the Cube Root of 144?
2.	How to Calculate the Cube Root of 144?
3.	Is the Cube Root of 144 Irrational?
4.	FAQs on Cube Root of 144

What is the Cube Root of 144?

The cube root of 144 is the number which when multiplied by itself three times gives the product as 144. Since 144 can be expressed as 2 × 2 × 2 × 2 × 3 × 3. Therefore, the cube root of 144 = ∛(2 × 2 × 2 × 2 × 3 × 3) = 5.2415.

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How to Calculate the Value of the Cube Root of 144?

Cube Root of 144 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 = 144
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 144]
⇒ x = 5
Therefore,
∛144 = 5 (5³ + 2 × 144)/(2 × 5³ + 144)) = 5.24
⇒ ∛144 ≈ 5.24
Therefore, the cube root of 144 is 5.24 approximately.

Is the Cube Root of 144 Irrational?

Yes, because ∛144 = ∛(2 × 2 × 2 × 2 × 3 × 3) = 2 ∛18 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 144 is an irrational number.

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Cube Root of 144 Solved Examples

Example 1: What is the value of ∛144 ÷ ∛(-144)?

Solution:

The cube root of -144 is equal to the negative of the cube root of 144.
⇒ ∛-144 = -∛144

Therefore,
⇒ ∛144/∛(-144) = ∛144/(-∛144) = -1
Example 2: The volume of a spherical ball is 144π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 144π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 144
⇒ R = ∛(3/4 × 144) = ∛(3/4) × ∛144 = 0.90856 × 5.24148 (∵ ∛(3/4) = 0.90856 and ∛144 = 5.24148)
⇒ R = 4.7622 in³
Example 3: Find the real root of the equation x³ − 144 = 0.

Solution:

x³ − 144 = 0 i.e. x³ = 144
Solving for x gives us,
x = ∛144, x = ∛144 × (-1 + √3i))/2 and x = ∛144 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛144
Therefore, the real root of the equation x³ − 144 = 0 is for x = ∛144 = 5.2415.

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FAQs on Cube Root of 144

What is the Value of the Cube Root of 144?

We can express 144 as 2 × 2 × 2 × 2 × 3 × 3 i.e. ∛144 = ∛(2 × 2 × 2 × 2 × 3 × 3) = 5.24148. Therefore, the value of the cube root of 144 is 5.24148.

Is 144 a Perfect Cube?

The number 144 on prime factorization gives 2 × 2 × 2 × 2 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 144 is irrational, hence 144 is not a perfect cube.

Why is the Value of the Cube Root of 144 Irrational?

The value of the cube root of 144 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛144 is irrational.

What is the Cube of the Cube Root of 144?

The cube of the cube root of 144 is the number 144 itself i.e. (∛144)³ = (144^1/3)³ = 144.

What is the Cube Root of -144?

The cube root of -144 is equal to the negative of the cube root of 144. Therefore, ∛-144 = -(∛144) = -(5.241) = -5.241.

How to Simplify the Cube Root of 144/216?

We know that the cube root of 144 is 5.24148 and the cube root of 216 is 6. Therefore, ∛(144/216) = (∛144)/(∛216) = 5.241/6 = 0.8735.

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