114 LearnersLast updated on May 26th, 2025
Cube Root of 328509
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 328509 and explain the methods used.
What is the Cube Root of 328509?
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, ∛328509 is written as 328509(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 328509, then y3 can be 328509. Since the cube root of 328509 is not an exact whole number, we can write it as approximately 69.9997, which rounds to 70.
Finding the Cube Root of 328509
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 328509. 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 cube number like 328509, we often follow Halley’s method.
Cube Root of 328509 by Halley’s method
Let's find the cube root of 328509 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 = 328509;
x = 70 (since 703 = 343000, which is close to 328509)
∛a ≅ 70((703 + 2 × 328509) / (2 × 703 + 328509))
∛328509 ≅ 70((343000 + 657018) / (686000 + 328509))
∛328509 ≅ 70.000
The cube root of 328509 is approximately 70.
Common Mistakes and How to Avoid Them in the Cube Root of 328509
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the 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 328509, which are not perfect cubes.
For example, they might assume that they would get an exact whole number for 328509. To avoid this error, it is essential to memorize that some numbers don't have a perfect cube root. The cube root of 328509 is approximately 70.
Cube Root of 328509 Examples:
Problem 1
Imagine you have a cube-shaped storage unit with a total volume of 328509 cubic centimeters. Find the length of one side of the storage unit equal to its cube root.
Side of the cube = ∛328509 = 70 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 70 units.
Problem 2
A company produces 328509 cubic meters of a material. Calculate the remaining material after using 10000 cubic meters.
The remaining material is 318509 cubic meters.
Explanation
To find the remaining material, subtract the used material from the total amount: 328509 - 10000 = 318509 cubic meters.
Problem 3
A container holds 328509 cubic meters of liquid. Another container holds a volume of 5000 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 333509 cubic meters.
Explanation
Let’s add the volume of both containers: 328509 + 5000 = 333509 cubic meters.
Problem 4
When the cube root of 328509 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 70 = 210 The cube of 210 = 9261000
Explanation
When we multiply the cube root of 328509 by 3, it results in a substantial increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(5000 + 323509).
∛(5000 + 323509) = ∛328509 ≈ 70
Explanation
As shown in the question ∛(5000 + 323509), we can simplify that by adding them.
So, 5000 + 323509 = 328509.
Then we use this step: ∛328509 ≈ 70 to get the answer.
FAQs on 328509 Cube Root
1.Can we find the Cube Root of 328509?
2.Why is Cube Root of 328509 irrational?
3.Is it possible to get the cube root of 328509 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 328509?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 328509?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 328509
- 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 328509(1/3), ⅓ is the exponent which denotes the cube root.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as simple fractions are irrational. For example, the cube root of 328509 is irrational because its decimal form goes on continuously without repeating.
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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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