116 LearnersLast updated on May 26th, 2025
Cube Root of 238328
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 238328 and explain the methods used.
What is the Cube Root of 238328?
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, ∛238328 is written as 238328(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 238328, then y3 can be 238328. Since the cube root of 238328 is an exact value, we can write it as 62.
Finding the Cube Root of 238328
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 238328. 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 perfect number, we can use the prime factorization method. Since 238328 is a perfect cube, we use this method.
Cube Root of 238328 by Prime Factorization
Let's find the cube root of 238328 using the prime factorization method.
Firstly, factorize 238328 into its prime components:
238328 = 2 × 2 × 2 × 7 × 7 × 7 × 11 × 11 × 11
Grouping the prime factors into triples gives: (2 × 2 × 2) × (7 × 7 × 7) × (11 × 11 × 11)
Taking one factor from each group, we get: 2 × 7 × 11 = 154
Therefore, the cube root of 238328 is 154.
Common Mistakes and How to Avoid Them in the Cube Root of 238328
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 approximate cube roots for perfect cube numbers.
Children sometimes try to calculate an approximate value for the cube root of numbers like 238328, which is actually a perfect cube. To avoid this error, verify whether the number is a perfect cube which can be exactly calculated as 154.
Cube Root of 238328 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 238328 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛238328 = 154 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 154 units.
Problem 2
A company manufactures 238328 cubic meters of material. Calculate the amount of material left after using 123456 cubic meters.
The amount of material left is 114872 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
238328 - 123456 = 114872 cubic meters.
Problem 3
A bottle holds 238328 cubic meters of volume. Another bottle holds a volume of 1000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 239328 cubic meters.
Explanation
Let’s add the volume of both bottles:
238328 + 1000 = 239328 cubic meters.
Problem 4
When the cube root of 238328 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 154 = 308 The cube of 308 = 3083 = 29104432
Explanation
When we multiply the cube root of 238328 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(238328 + 32768).
∛(238328 + 32768) = ∛271096 ≈ 140.89
Explanation
As shown in the question ∛(238328 + 32768), we can simplify that by adding them.
So, 238328 + 32768 = 271096.
Then we use this step: ∛271096 ≈ 140.89 to get the answer.
FAQs on 238328 Cube Root
1.Can we find the Cube Root of 238328?
2.Why is Cube Root of 238328 rational?
3.Is it possible to get the cube root of 238328 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 Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube Root of 238328?
8.How do technology and digital tools in Australia support learning Algebra and Cube Root of 238328?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube Root of 238328
- 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: 154^3 = 238328, therefore, 238328 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), ⅓ 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 (∛).
- Rational number: A number is rational if it can be expressed as a fraction or a whole number. The cube root of 238328 is rational because it is an exact whole number.
Explore More algebra
Previous to Cube Root of 238328
About BrightChamps in Australia
Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
