111 LearnersLast updated on May 26th, 2025
Cube Root of 11664
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 11664 and explain the methods used.
What is the Cube Root of 11664?
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, ∛11664 is written as 11664(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 11664, then y3 can be 11664. The cube root of 11664 is an exact value, which is 24.
Finding the Cube Root of 11664
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 11664. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 11664 is a perfect cube, we can primarily use the prime factorization method to find its cube root.
Cube Root of 11664 by Prime Factorization Method
Let's find the cube root of 11664 using the prime factorization method.
The process involves expressing 11664 as a product of its prime factors:
11664 = 22 × 36
To find the cube root, we take one-third of the power of each prime factor:
∛11664 = 2(2/3) × 3(6/3)
= 20.67 × 32 = 24
Therefore, the cube root of 11664 is 24.
Common Mistakes and How to Avoid Them in the Cube Root of 11664
Finding the perfect cube of a number without any errors can be a difficult task for the 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 without using prime factorization.
Students sometimes overlook the method of prime factorization for perfect cubes like 11664.
For example, they might attempt approximation, which is unnecessary for perfect cubes. To avoid this error, remember that prime factorization is ideal for perfect cubes like 11664.
Cube Root of 11664 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 11664 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛11664 = 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 24 units.
Problem 2
A company manufactures 11664 cubic meters of material. Calculate the amount of material left after using 5000 cubic meters.
The amount of material left is 6664 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
11664 - 5000 = 6664 cubic meters.
Problem 3
A bottle holds 11664 cubic meters of volume. Another bottle holds a volume of 336 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 12000 cubic meters.
Explanation
Let’s add the volume of both bottles:
11664 + 336 = 12000 cubic meters.
Problem 4
When the cube root of 11664 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 11664 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(1296 + 10368).
∛(1296 + 10368) = ∛11664 = 24
Explanation
As shown in the question ∛(1296 + 10368), we can simplify that by adding them.
So, 1296 + 10368 = 11664.
Then we use this step: ∛11664 = 24 to get the answer.
FAQs on 11664 Cube Root
1.Can we find the Cube Root of 11664?
2.Why is Cube Root of 11664 rational?
3.Is it possible to get the cube root of 11664 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 11664?
8.How do technology and digital tools in Australia support learning Algebra and Cube Root of 11664?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube Root of 11664
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 11664(1/3), ⅓ is the exponent which denotes the cube root of 11664.
Radical sign: The symbol that is used to represent a root which is expressed as (∛).
Rational number: Numbers that can be expressed as a fraction or whole number. For example, the cube root of 11664 is rational because it is 24.
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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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