131 LearnersLast updated on May 26th, 2025
Cube Root of 474552
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 474552 and explain the methods used.
What is the Cube Root of 474552?
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, ∛474552 is written as 474552(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 474552, then y3 can be 474552. Since the cube root of 474552 is an exact value, we can write it as 78.
Finding the Cube Root of 474552
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 474552. 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 follow the prime factorization method. Since 474552 is a perfect cube, we can use this method.
Cube Root of 474552 by Prime Factorization
Let's find the cube root of 474552 using the prime factorization method.
First, we find the prime factors of 474552: 474552 = 2 × 2 × 2 × 3 × 3 × 3 × 29 × 29 × 29
Grouping the factors into triples, we have: (2 × 2 × 2) × (3 × 3 × 3) × (29 × 29 × 29)
Taking one factor from each group gives us: 2 × 3 × 29 = 78
Therefore, ∛474552 = 78.
Common Mistakes and How to Avoid Them in the Cube Root of 474552
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 perfect cube roots for non-perfect cube numbers.
Students sometimes assume non-perfect cubes have whole number roots. However, 474552 is a perfect cube, and its cube root is exactly 78.
Cube Root of 474552 Examples:
Problem 1
Imagine you have a cube-shaped storage room with a total volume of 474552 cubic meters. Find the length of one side of the room equal to its cube root.
Side of the cube = ∛474552 = 78 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 78 meters.
Problem 2
A factory produces 474552 cubic meters of material. Calculate the amount of material left after using 100000 cubic meters.
The amount of material left is 374552 cubic meters.
Explanation
To find the remaining material, subtract the used material from the total amount: 474552 - 100000 = 374552 cubic meters.
Problem 3
A tank holds 474552 cubic meters of water. Another tank holds a volume of 50000 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 524552 cubic meters.
Explanation
Explanation: Let’s add the volume of both tanks: 474552 + 50000 = 524552 cubic meters.
Problem 4
When the cube root of 474552 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 78 = 156 The cube of 156 = 3796416
Explanation
When we multiply the cube root of 474552 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(50000 + 424552).
∛(50000 + 424552) = ∛474552 = 78
Explanation
As shown in the question ∛(50000 + 424552), we can simplify that by adding them.
So, 50000 + 424552 = 474552.
Then we use this step: ∛474552 = 78 to get the answer.
FAQs on 474552 Cube Root
1.Can we find the Cube Root of 474552?
2.Why is the Cube Root of 474552 rational?
3.Is it possible to get the cube root of 474552 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 Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Cube Root of 474552?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube Root of 474552?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for Cube Root of 474552
- 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: 78 × 78 × 78 = 474552, therefore, 474552 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 474552(1/3), ⅓ is the exponent which denotes the cube root of 474552.
- 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. The cube root of 474552 is rational because it is 78.
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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.
