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102 LearnersLast updated on April 28th, 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
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.
Explanation
Problem 2
A company manufactures 74088 cubic meters of material. Calculate the amount of material left after using 12345 cubic meters.
Explanation
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?
Explanation
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?
Explanation
Problem 5
Find ∛(50000 + 24088).
Explanation
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?
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
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.
