Cube Root of 432

The cube root of 432 is a natural number that has a cube of 432. 432’s cube root has a value of around 7.559. Finding an integer’s cube root is the opposite of cubing it. The square root and cube root are denoted by the radicals “√” and “∛”, respectively. The cube root of 432 is expressed exponentially by the number 4321/3. Let’s look at numerous approaches to finding the cube root of 432.

Cube Root of 432
  • In decimal form: 7.559
  • In radical form: ∛432 or 6 ∛2.
Cube of 432 80621568

Also, read:How to Find Cube Root?

What is the Cube Root of 432?

The cube root of 432 is the number whose cube is 432. The cube of an integer always generates a perfect cube. Since 432 is not the cube of any integer, it is not a perfect cube number. The number 432 is also composite. A thorough explanation of how to compute the cube root of 432 is given in this article.

Cube Root of 432

Also, try out:Cube Root Calculator

How to Find the Cube Root of 432?

Let’s now compute the cube root of 432. In this article, we’ll analyse it from several perspectives.

Finding Cube Root of 432 by Prime Factorisation Method

The procedures for implementing the prime factorisation technique to calculate an integer’s cube root are outlined below.

  • Get the prime factors of the number
  • Make a group of three for each prime factor in the prime factorisation
  • On each group, one instance of the factor is picked, and all the prime factors are then multiplied. A factor cannot be further simplified if it cannot be broken into three

Let’s compute the cube root of 432 using the prime factorisation method.

As we are all aware, the prime factorisation of 432 is 2 × 2 × 2 × 2 × 3 × 3 × 3.

Therefore, the radical representation of the cube root of 432 is:

∛432 = ∛(2 × 2 × 2 × 2 × 3 × 3 × 3) = 2 × 3 × ∛2 = 6∛2.

6∛2 cannot be reduced further. Hence its cube root is also an irrational number.

Finding Cube Root of 432 by Approximation Method

Using Halley’s approach, which is also known as an approximation method, one can determine the cube root of any integer. Using Halley’s approach, the cube root of 432 may be determined as illustrated below:

Halley’s Cube Root Formula:

\(\begin{array}{l}\sqrt[3]{a}\approx x\left [ \frac{x^{3}+2a}{2x^{3}+a} \right ]\end{array} \)

Where

The calculation for the cube root that is needed is represented by the letter “a.”

To determine the projected value, the cube root of the closest perfect cube, “x,” should be used.

Here, a = 432

If x = 7, then we will obtain 73 = 343 < 432.

Using Halley’s formula, the results of computing the cube root of 432 are remarkably comparable.

∛432 = 7[(73 + 2 × 432)/(2 × 73 + 432)]

∛432 = 7[(343 + 864)/(686 + 432)]

∛432 = 7[1207/1118]

∛432 = 7[1.079] ≈ 7.553, which is near to the cube root of 432.

By using the Halley formula, we can establish that 7.553 is the value that corresponds to the cube root of 432.

Video Lesson on Finding Cube Roots

94,583

Related Articles

Solved Examples on Cube Root of 432

Example 1:

Determine the value of x if the equation ∛432x = 12(7.559).

Solution:

Equation given: ∛432x = 12(7.559).

It is already well known that the cube root of 432 is extremely similar to the value 7.559.

If we plug in the value ∛432 = 7.559 into the equation given above, we get the answer

7.559 x = 12(7.559)

⇒ x = [12(7.559)] /7.559

⇒ x = 12.

Therefore, x is equal to 12

Example 2:

Determine the lowest integer that, multiplied by 432, produces a number that is a perfect cube.

Solution:

As we know, 2 × 2 × 2 × 2 × 3 × 3 × 3 is the prime factorisation of 432.

To calculate the cube root of 432, each element has to be grouped by three first. As a consequence of this, we need to multiply 432 by 2 × 2.

As a result, we get

432 × 2 × 2 = 432 × 4 = 1728

Therefore, the number 1728 is a perfect cube number.

So, the cube root of 1728 is ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 2 × 2 × 3 = 12

As a result, the least number that can be multiplied by 432 to obtain the perfect cube number is 4.

Example 3:

Find the lengths of the cube’s sides if its volume is 432 cm3.

Solution:

Assuming that “a” denotes the length of one of the cube’s sides, and the solution is as follows:

This suggests that the volume of the cube is a3 = 432 cm3.

By taking the cube roots on both sides of the equation, we obtain

a = ∛432 = 7.559 (approximately).

As a result, the value of “a” is about 7.559.

Frequently Asked Questions on Cube Root of 432

Q1

If you take the cube root of 432, what do you get as a result?

The value of the cube root of 432 is about 7.559.

Q2

How about the number 432? Is it a perfect cube?

Since 432 cannot be stated as the cube of any integer, it cannot be considered a perfect cube.

Q3

What is the value of the cube root of -432?

The value -7.559 is approximately equivalent to the cube root of -432.
It means that, ∛-432 = -∛432 = -7.559.

Q4

What result do you get if you take the cube root of 432 and add it to two?

When you add two to the value you get when you take the cube root of 432, you get 9.559.
As we know that ∛432 = 7.559.
So, 2 + 7.559 = 9.559.

Q5

What is the most basic representation of the cube root of 432 in radical form?

The simplest radical, 6∛2, is used to represent the cube root of 432.