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Cube Root of 432

The value of the cube root of 432 rounded to 4 decimal places is 7.5595. It is the real solution of the equation x³ = 432. The cube root of 432 is expressed as ∛432 or 6 ∛2 in the radical form and as (432)^⅓ or (432)^0.33 in the exponent form. The prime factorization of 432 is 2 × 2 × 2 × 2 × 3 × 3 × 3, hence, the cube root of 432 in its lowest radical form is expressed as 6 ∛2.

Cube root of 432: 7.559526299
Cube root of 432 in Exponential Form: (432)^⅓
Cube root of 432 in Radical Form: ∛432 or 6 ∛2

Cube Root of 432

1.	What is the Cube Root of 432?
2.	How to Calculate the Cube Root of 432?
3.	Is the Cube Root of 432 Irrational?
4.	FAQs on Cube Root of 432

What is the Cube Root of 432?

The cube root of 432 is the number which when multiplied by itself three times gives the product as 432. Since 432 can be expressed as 2 × 2 × 2 × 2 × 3 × 3 × 3. Therefore, the cube root of 432 = ∛(2 × 2 × 2 × 2 × 3 × 3 × 3) = 7.5595.

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How to Calculate the Value of the Cube Root of 432?

Cube Root of 432 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 = 432
Let us assume x as 7
[∵ 7³ = 343 and 343 is the nearest perfect cube that is less than 432]
⇒ x = 7
Therefore,
∛432 = 7 (7³ + 2 × 432)/(2 × 7³ + 432)) = 7.56
⇒ ∛432 ≈ 7.56
Therefore, the cube root of 432 is 7.56 approximately.

Is the Cube Root of 432 Irrational?

Yes, because ∛432 = ∛(2 × 2 × 2 × 2 × 3 × 3 × 3) = 6 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 432 is an irrational number.

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Cube Root of 432 Solved Examples

Example 1: What is the value of ∛432 + ∛(-432)?

Solution:

The cube root of -432 is equal to the negative of the cube root of 432.
i.e. ∛-432 = -∛432

Therefore, ∛432 + ∛(-432) = ∛432 - ∛432 = 0
Example 2: Given the volume of a cube is 432 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 432 in³ = a³
⇒ a³ = 432
Cube rooting on both sides,
⇒ a = ∛432 in
Since the cube root of 432 is 7.56, therefore, the length of the side of the cube is 7.56 in.
Example 3: Find the real root of the equation x³ − 432 = 0.

Solution:

x³ − 432 = 0 i.e. x³ = 432
Solving for x gives us,
x = ∛432, x = ∛432 × (-1 + √3i))/2 and x = ∛432 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛432
Therefore, the real root of the equation x³ − 432 = 0 is for x = ∛432 = 7.5595.

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FAQs on Cube Root of 432

What is the Value of the Cube Root of 432?

We can express 432 as 2 × 2 × 2 × 2 × 3 × 3 × 3 i.e. ∛432 = ∛(2 × 2 × 2 × 2 × 3 × 3 × 3) = 7.55953. Therefore, the value of the cube root of 432 is 7.55953.

Why is the Value of the Cube Root of 432 Irrational?

The value of the cube root of 432 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛432 is irrational.

Is 432 a Perfect Cube?

The number 432 on prime factorization gives 2 × 2 × 2 × 2 × 3 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 432 is irrational, hence 432 is not a perfect cube.

What is the Cube Root of -432?

The cube root of -432 is equal to the negative of the cube root of 432. Therefore, ∛-432 = -(∛432) = -(7.56) = -7.56.

How to Simplify the Cube Root of 432/8?

We know that the cube root of 432 is 7.55953 and the cube root of 8 is 2. Therefore, ∛(432/8) = (∛432)/(∛8) = 7.56/2 = 3.78.

What is the Value of 3 Plus 4 Cube Root 432?

The value of ∛432 is 7.56. So, 3 + 4 × ∛432 = 3 + 4 × 7.56 = 33.239999999999995. Hence, the value of 3 plus 4 cube root 432 is 33.239999999999995.

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