103 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 = -9261. The cube root of -9261 is an exact value, which is -21.
Finding the Cube Root of -9261
Finding the cube root of a number means identifying the number that must be multiplied three times to get 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
To find the cube root of a perfect cube, like -9261, we can use the prime factorization method.
Cube Root of -9261 by Prime Factorization Method
Let's find the cube root of -9261 using the prime factorization method:
1. Prime factorize -9261: -9261 = -1 × 21 × 21 × 21
2. The prime factors are grouped into triples: (-1 × 21) × (21²)
3. The cube root is the product of one factor from each group: ∛(-9261) = -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 root 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 the cube root of a negative number incorrectly.
Children often forget that the cube root of a negative number is negative.
For example, they might not realize that the cube root of -9261 is -21. To avoid this error, remember that the cube root of a negative number is also negative.
Mistake 2
Ignoring the exponent form
Most of us might forget that the cube root can also be written in exponent form.
For example: Forgetting that the cube root of -9261 is (-9261)^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
To avoid this, children should remember that the cube root of -9261 is the number they multiply by itself three times to get -9261.
Mistake 4
Using approximation for perfect cubes
Instead of using the prime factorization method for perfect cubes, children end up using approximation methods.
For example, they might try to approximate the cube root of -9261. Remember that for perfect cubes, the exact cube root can be found using prime factorization.
Mistake 5
Rounding too early
For perfect cubes like -9261, rounding errors are not a concern, but when using other methods, rounding too early can lead to inaccuracies. Always carry calculations through to the end before rounding if necessary.
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 box equal to its cube root.
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 -21 units.
Problem 2
A company manufactures -9261 cubic meters of material. Calculate the amount of material left after using -3000 cubic meters.
The amount of material left is -6261 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
-9261 - (-3000)
= -6261 cubic meters.
Problem 3
A bottle holds -9261 cubic meters of volume. Another bottle holds a volume of -1000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is -10261 cubic meters.
Explanation
Explanation: Let’s add the volume of both bottles: -9261 + (-1000) = -10261 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 cube because the cube increases exponentially.
Problem 5
Find ∛(-92 + -169).
∛(-92 + -169) = ∛(-261) ≈ -6.41
Explanation
As shown in the question ∛(-92 + -169), we can simplify that by adding them: -92 + -169 = -261.
Then we use this step: ∛(-261) ≈ -6.41 to get the answer.
FAQs on -9261 Cube Root
1.Can we find the Cube Root of -9261?
2.Why is Cube Root of -9261 a rational number?
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?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube Root of -9261?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube Root of -9261?
9.Does learning Algebra support future career opportunities for students in Vietnam?
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.
- 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 (∛).
- Rational number: A number that can be expressed as a fraction or a whole number. For example, the cube root of -9261 is rational because it is -21.
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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.
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