108 LearnersLast updated on May 26th, 2025
Cube Root of 8640
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 8640 and explain the methods used.
What is the Cube Root of 8640?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.
In exponential form, ∛8640 is written as 8640(1/3). The cube root is just the opposite operation of finding the cube of a number. For example, assume ‘y’ as the cube root of 8640, then y3 can be 8640. Since the cube root of 8640 is not an exact whole number, we can write it as approximately 20.4722.
Finding the Cube Root of 8640
Finding the cube root of a number involves identifying the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of 8640. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a non-perfect number, we often follow Halley’s method. Since 8640 is not a perfect cube, we use Halley’s method.
Cube Root of 8640 by Halley’s method
Let's find the cube root of 8640 using Halley’s method.
The formula is: ∛a ≅ x((x3 + 2a) / (2x3 + a))
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting a = 8640;
x = 20
∛a ≅ 20((203 + 2 × 8640) / (2 × 203 + 8640))
∛8640 ≅ 20.472
The cube root of 8640 is approximately 20.4722.
Common Mistakes and How to Avoid Them in the Cube Root of 8640
Finding the cube root of a number without any errors can be a challenging task for students. This happens for many reasons. Here are a few mistakes students commonly make and the ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers like 8640, which are not perfect cubes.
For example, they assume that they would get an exact whole number for 8640 like they get for 27 (since 33 = 27). To avoid this error, memorize that some numbers don't have a perfect cube root, that is, the cube root of 8640 is approximately 20.472.
Cube Root of 8640 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 8640 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛8640 ≈ 20.47 units
Explanation
To find the side of the cube, we need to find the cube root of the given volume.
Therefore, the side length of the cube is approximately 20.47 units.
Problem 2
A company manufactures 8640 cubic meters of material. Calculate the amount of material left after using 3000 cubic meters.
The amount of material left is 5640 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
8640 - 3000 = 5640 cubic meters.
Problem 3
A bottle holds 8640 cubic meters of volume. Another bottle holds a volume of 360 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 9000 cubic meters.
Explanation
Let’s add the volume of both bottles:
8640 + 360 = 9000 cubic meters.
Problem 4
When the cube root of 8640 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 20.47 ≈ 40.94 The cube of 40.94 ≈ 68659.6
Explanation
When we multiply the cube root of 8640 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(8000 + 640).
∛(8000 + 640) = ∛8640 ≈ 20.47
Explanation
As shown in the question ∛(8000 + 640), we can simplify that by adding them.
So, 8000 + 640 = 8640.
Then we use this step: ∛8640 ≈ 20.47 to get the answer.
FAQs on 8640 Cube Root
1.Can we find the Cube Root of 8640?
2.Why is Cube Root of 8640 irrational?
3.Is it possible to get the cube root of 8640 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube Root of 8640?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 8640?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 8640
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a(1/3), 1/3 is the exponent which denotes the cube root of a.
- Radical sign: The symbol that is used to represent a root, which is expressed as (∛).
- Irrational number: Numbers that cannot be put in fractional forms are irrational. For example, the cube root of 8640 is irrational because its decimal form goes on continuously without repeating the numbers.
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Jaskaran Singh Saluja
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Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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