110 LearnersLast updated on May 26th, 2025
Cube Root of 29791
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 29791 and explain the methods used.
What is the Cube Root of 29791?
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, ∛29791 is written as 29791(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 29791, then y3 can be 29791. Since the cube root of 29791 is an exact value, it is 31.
Finding the Cube Root of 29791
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 29791. 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 follow the prime factorization method. Since 29791 is a perfect cube, we use the prime factorization method.
Cube Root of 29791 by Prime Factorization Method
Let's find the cube root of 29791 using the prime factorization method.
First, perform the prime factorization of 29791:
29791 = 31 × 31 × 31
Since all the prime factors are grouped into triples, the cube root of 29791 is 31.
Common Mistakes and How to Avoid Them in the Cube Root of 29791
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 cube roots for numbers they assume are non-perfect cubes.
Children sometimes assume numbers like 29791, which are perfect cubes, are not, leading to unnecessary approximation. To avoid this error, verify if a number is a perfect cube through methods like prime factorization.
Cube Root of 29791 Examples:
Problem 1
Imagine you have a cube-shaped room that has a total volume of 29791 cubic meters. Find the length of one side of the room equal to its cube root.
Side of the cube = ∛29791 = 31 meters
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 31 meters.
Problem 2
A warehouse stores 29791 cubic meters of material. Calculate the amount of material left after using 10000 cubic meters.
The amount of material left is 19791 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
29791 - 10000 = 19791 cubic meters.
Problem 3
A tank holds 29791 cubic meters of water. Another tank holds a volume of 5000 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 34791 cubic meters.
Explanation
Let’s add the volume of both tanks:
29791 + 5000 = 34791 cubic meters.
Problem 4
When the cube root of 29791 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 31 = 62
The cube of 62 = 238328
Explanation
When we multiply the cube root of 29791 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(1500+1500).
∛(1500+1500) = ∛3000 ≈ 14.42
Explanation
As shown in the question ∛(1500+1500), we can simplify that by adding them.
So, 1500 + 1500 = 3000.
Then we use this step: ∛3000 ≈ 14.42 to get the answer.
FAQs on 29791 Cube Root
1.Can we find the Cube Root of 29791?
2.Why is Cube Root of 29791 a rational number?
3.Is it possible to get the cube root of 29791 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 United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube Root of 29791?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 29791?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 29791
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. For example: 31 × 31 × 31 = 29791, therefore, 29791 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), 1/3 is the exponent which denotes the cube root of a.
Radical sign: The symbol that is used to represent a root is expressed as (∛).
Rational number: A number that can be expressed as a ratio of integers. The cube root of 29791 is rational because it equals 31.
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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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