122 LearnersLast updated on May 26th, 2025
Cube Root of 13824
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 13824 and explain the methods used.
What is the Cube Root of 13824?
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, ∛13824 is written as 13824(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 13824, then y3 can be 13824. Since 13824 is a perfect cube, the cube root of 13824 is exactly 24.
Finding the Cube Root of 13824
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 13824. 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 number like 13824, we can use the prime factorization method for an exact value.
Cube Root of 13824 by Prime Factorization Method
Let's find the cube root of 13824 using the prime factorization method. 1.
Start by breaking down 13824 into its prime factors:
13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 2.
Group the prime factors into triples:
(2 × 2 × 2) × (2 × 2 × 2) × (2 × 2) × (3 × 3 × 3) 3.
Take one factor from each group: 2 × 2 × 3 = 12.
The cube root of 13824 is 24.
Common Mistakes and How to Avoid Them in the Cube Root of 13824
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 sometimes try to calculate an exact whole number for the cube root of numbers that are not perfect cubes.
For example, they assume they would get an exact whole number for a non-perfect cube like 39. To avoid this error, remember that some numbers don't have a perfect cube root. However, 13824 is a perfect cube, yielding a precise cube root of 24.
Cube Root of 13824 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 13824 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛13824 = 24 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 24 units.
Problem 2
A company manufactures 13824 cubic meters of material. Calculate the amount of material left after using 12000 cubic meters.
The amount of material left is 1824 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
13824 - 12000 = 1824 cubic meters.
Problem 3
A bottle holds 13824 cubic meters of volume. Another bottle holds a volume of 576 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 14400 cubic meters.
Explanation
Let’s add the volume of both bottles:
13824 + 576 = 14400 cubic meters.
Problem 4
When the cube root of 13824 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 24 = 48
The cube of 48 = 110592
Explanation
When we multiply the cube root of 13824 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(2304+11520).
∛(2304+11520) = ∛13824 = 24
Explanation
As shown in the question ∛(2304+11520), we can simplify that by adding them.
So, 2304 + 11520 = 13824.
Then we use this step: ∛13824 = 24 to get the answer.
FAQs on 13824 Cube Root
1.Can we find the Cube Root of 13824?
2.Why is Cube Root of 13824 not irrational?
3.Is it possible to get the cube root of 13824 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 Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Cube Root of 13824?
8.How do technology and digital tools in Oman support learning Algebra and Cube Root of 13824?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube Root of 13824
- 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: 24 × 24 × 24 = 13824, therefore, 13824 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 (∛).
- Prime factorization: A method of expressing a number as the product of its prime numbers. It is useful in finding the cube root of perfect cubes.
Explore More algebra
Previous to Cube Root of 13824
About BrightChamps in Oman
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.
