106 LearnersLast updated on May 26th, 2025
Cube Root of 9261
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 9261 and explain the methods used.
What is the Cube Root of 9261?
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, ∛9261 is written as 9261(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 9261, then y3 can be 9261. Since 9261 is a perfect cube, we find that ∛9261 is exactly 21.
Finding the Cube Root of 9261
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 9261. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 9261 is a perfect cube, we can effectively use the prime factorization method.
Cube Root of 9261 by Prime Factorization
Let's find the cube root of 9261 using the prime factorization method.
First, find the prime factors of 9261:
9261 ÷ 3 = 3087
3087 ÷ 3 = 1029
1029 ÷ 3 = 343
343 ÷ 7 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factorization of 9261 is 33 × 73.
To find the cube root, take one factor from each triplet of the same number:
∛(33× 73) = 3 × 7 = 21
The cube root of 9261 is 21.
Common Mistakes and How to Avoid Them in the Cube Root of 9261
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 students commonly make and the ways to avoid them:
Mistake 1
Trying to find approximate cube roots for perfect cube numbers.
Children sometimes assume that the cube root of a perfect cube like 9261 will be an approximate value.
For example: They assume they need to approximate the cube root of 9261. To avoid this error, remember that the cube root of 9261 is exactly 21.
Cube Root of 9261 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 9261 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛9261 = 21 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 21 units.
Problem 2
A company manufactures 9261 cubic meters of material. Calculate the amount of material left after using 2000 cubic meters.
The amount of material left is 7261 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
9261 - 2000 = 7261 cubic meters.
Problem 3
A bottle holds 9261 cubic meters of volume. Another bottle holds a volume of 739 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 10000 cubic meters.
Explanation
Let’s add the volume of both bottles:
9261 + 739 = 10000 cubic meters.
Problem 4
When the cube root of 9261 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 21 = 42 The cube of 42 = 74088
Explanation
When we multiply the cube root of 9261 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(5000 + 4261).
∛(5000 + 4261) = ∛9261 = 21
Explanation
As shown in the question ∛(5000 + 4261), we can simplify that by adding them.
So, 5000 + 4261 = 9261.
Then, we find that ∛9261 = 21, which is the answer.
FAQs on 9261 Cube Root
1.Can we find the Cube Root of 9261?
2.Why is Cube Root of 9261 rational?
3.Is it possible to get the cube root of 9261 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 9261
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: 21 × 21 × 21 = 9261, therefore, 9261 is a perfect cube.
Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 9261(1/3), ⅓ is the exponent which denotes the cube root of 9261.
Radical sign: The symbol that is used to represent a root which is expressed as (∛).
Rational number: A number that can be expressed as a fraction or ratio of two integers. The cube root of 9261 is rational because it is a whole number.
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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.
