114 LearnersLast updated on May 26th, 2025
Cube Root of 24389
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 24389 and explain the methods used.
What is the Cube Root of 24389?
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, ∛24389 is written as 24389(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 24389, then y3 can be 24389. Since 24389 is a perfect cube, the cube root of 24389 is exactly 29.
Finding the Cube Root of 24389
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 24389. 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 cube, we can use the prime factorization method. Since 24389 is a perfect cube, this method is effective.
Cube Root of 24389 by Prime Factorization Method
Let's find the cube root of 24389 using the prime factorization method.
We break down 24389 into its prime factors:
24389 = 29 × 29 × 29
Since we have three 29s, the cube root is the number that appears thrice in the factorization.
∛24389 = 29
The cube root of 24389 is exactly 29.
Common Mistakes and How to Avoid Them in the Cube Root of 24389
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 non-integer cube roots for perfect cube numbers.
Children may incorrectly assume that a perfect cube like 24389 does not have an integer cube root.
For example, they might not realize that 24389 has an exact whole number cube root of 29. To avoid this error, ensure to recognize when a number is a perfect cube, yielding an integer root.
Cube Root of 24389 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 24389 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛24389 = 29 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 exactly 29 units.
Problem 2
A company manufactures 24389 cubic meters of material. Calculate the amount of material left after using 1000 cubic meters.
The amount of material left is 23389 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
24389 - 1000 = 23389 cubic meters.
Problem 3
A bottle holds 24389 cubic meters of volume. Another bottle holds a volume of 111 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 24500 cubic meters.
Explanation
Let’s add the volume of both bottles:
24389 + 111 = 24500 cubic meters.
Problem 4
When the cube root of 24389 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 29 = 87
The cube of 87 = 658503
Explanation
When we multiply the cube root of 24389 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(12000 + 12389).
∛(12000 + 12389) = ∛24389 = 29
Explanation
As shown in the question ∛(12000 + 12389), we can simplify that by adding them.
So, 12000 + 12389 = 24389.
Then we use this step: ∛24389 = 29 to get the answer.
FAQs on 24389 Cube Root
1.Can we find the Cube Root of 24389?
2.Why is Cube Root of 24389 rational?
3.Is it possible to get the cube root of 24389 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 24389?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 24389?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 24389
- 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. For example, 29 × 29 × 29 = 24389.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In ∛24389, ⅓ is the exponent which denotes the cube root of 24389.
- Radical sign: The symbol that is used to represent a root, expressed as (∛).
- Rational number: The numbers that can be expressed as a fraction. For example, the cube root of 24389 is rational because it is 29, which can be represented as 29/1.
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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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