129 LearnersLast updated on May 26th, 2025
Cube Root of 21952
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 21952 and explain the methods used.
What is the Cube Root of 21952?
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, ∛21952 is written as 21952(1/3). The cube root is just the opposite operation of finding the cube of a number. For example, assume ‘y’ is the cube root of 21952, then y3 can be 21952. The cube root of 21952 is an exact value and is 28.
Finding the Cube Root of 21952
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 21952. 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 often use the prime factorization method. Since 21952 is a perfect cube, we can use the prime factorization method.
Cube Root of 21952 by Prime Factorization Method
Let's find the cube root of 21952 using the prime factorization method.
First, we perform the prime factorization of 21952:
21952 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7
Grouping the factors in triples: 21952 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (7 × 7 × 7) = 23 × 23 × 23 × 73
The cube root is: ∛21952 = 2 × 2 × 2 × 7 = 28
The cube root of 21952 is 28.
Common Mistakes and How to Avoid Them in the Cube Root of 21952
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-perfect cube roots for perfect cube numbers.
Children sometimes assume that a number like 21952 is not a perfect cube and try to approximate its cube root. However, 21952 is a perfect cube, and its cube root is exactly 28. To avoid this error, check if the number can be factored into a perfect cube.
Cube Root of 21952 Examples:
Problem 1
Imagine you have a cube-shaped object that has a total volume of 21952 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛21952 = 28 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 28 units.
Problem 2
A company manufactures 21952 cubic meters of material. Calculate the amount of material left after using 2000 cubic meters.
The amount of material left is 19952 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
21952 - 2000 = 19952 cubic meters.
Problem 3
A warehouse holds a volume of 21952 cubic meters of goods. Another warehouse holds a volume of 8000 cubic meters. What would be the total volume if the warehouses are combined?
The total volume of the combined warehouses is 29952 cubic meters.
Explanation
Let’s add the volume of both warehouses:
21952 + 8000 = 29952 cubic meters.
Problem 4
When the cube root of 21952 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 28 = 84
The cube of 84 = 592704
Explanation
When we multiply the cube root of 21952 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(10000 + 11952).
∛(10000 + 11952) = ∛21952 = 28
Explanation
As shown in the question ∛(10000 + 11952), we can simplify that by adding them.
So, 10000 + 11952 = 21952.
Then we use this step: ∛21952 = 28 to get the answer.
FAQs on 21952 Cube Root
1.Can we find the Cube Root of 21952?
2.Why is the Cube Root of 21952 not irrational?
3.Is it possible to get the cube root of 21952 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 21952
- Cube root: The number that, when multiplied by itself three times, results in the given number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. For example, 2 × 2 × 2 = 8, so 8 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 used to represent a root, expressed as (∛).
- Prime factorization: A method of expressing a number as the product of its prime factors, useful for 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.
