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102 LearnersLast updated on April 28th, 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
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.
Explanation
Problem 2
A company manufactures 13824 cubic meters of material. Calculate the amount of material left after using 12000 cubic meters.
Explanation
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?
Explanation
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?
Explanation
Problem 5
Find ∛(2304+11520).
Explanation
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?
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.
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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.
