123 LearnersLast updated on May 26th, 2025
Cube Root of 74088
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 74088 and explain the methods used.
What is the Cube Root of 74088?
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, ∛74088 is written as 74088(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 74088, then y³ can be 74088. Since the cube root of 74088 is an exact value, it can be written as 42.
Finding the Cube Root of 74088
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 74088. 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 number, we often use the prime factorization method. Since 74088 is a perfect cube, we use the prime factorization method.
Cube Root of 74088 by Prime Factorization
Let's find the cube root of 74088 using the prime factorization method:
First, factorize 74088 into its prime factors: 74088 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7
Grouping the factors into triples, we have: (2 × 2 × 2) × (3 × 3 × 3) × (7 × 7 × 7)
Taking one number from each triplet, we get: 2 × 3 × 7 = 42
Thus, the cube root of 74088 is 42.
Common Mistakes and How to Avoid Them in the Cube Root of 74088
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.
Students sometimes assume they need an approximate value for cube roots of numbers like 74088, which are perfect cubes.
For example, they might not realize that 74088 has an exact cube root of 42. To avoid this error, verify if a number is a perfect cube when possible.
Cube Root of 74088 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 74088 cubic centimeters. Find the length of one side of the toy.
Side of the cube = ∛74088 = 42 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 42 units.
Problem 2
A company manufactures 74088 cubic meters of material. Calculate the amount of material left after using 12345 cubic meters.
The amount of material left is 61743 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
74088 - 12345 = 61743 cubic meters.
Problem 3
A bottle holds 74088 cubic meters of volume. Another bottle holds a volume of 8000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 82088 cubic meters.
Explanation
Let’s add the volume of both bottles:
74088 + 8000 = 82088 cubic meters.
Problem 4
When the cube root of 74088 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 42 = 84 The cube of 84 = 592704
Explanation
When we multiply the cube root of 74088 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(50000 + 24088).
∛(50000 + 24088) = ∛74088 = 42
Explanation
As shown in the question ∛(50000 + 24088), we can simplify that by adding them.
So, 50000 + 24088 = 74088.
Then we use this step: ∛74088 = 42 to get the answer.
FAQs on 74088 Cube Root
1.Can we find the Cube Root of 74088?
2.Why is Cube Root of 74088 not irrational?
3.Is it possible to get the cube root of 74088 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 Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Cube Root of 74088?
8.How do technology and digital tools in Canada support learning Algebra and Cube Root of 74088?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube Root of 74088
- 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, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. For example, 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, expressed as (∛).
- Prime Factorization: A method of expressing a number as the product of its prime factors, often used to find exact cube roots for perfect cubes.
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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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