112 LearnersLast updated on May 26th, 2025
Cube Root of 2460375
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 2460375 and explain the methods used.
What is the Cube Root of 2460375?
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, ∛2460375 is written as 2460375(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 2460375, then y3 can be 2460375. Since the cube root of 2460375 is an exact whole number, we can find it precisely.
Finding the Cube Root of 2460375
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 2460375. 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 can use the prime factorization method. Since 2460375 is a perfect cube, we will use this method.
Cube Root of 2460375 by Prime Factorization
Let's find the cube root of 2460375 using the prime factorization method.
First, perform the prime factorization of 2460375: 2460375 = 3 × 3 × 3 × 5 × 5 × 5 × 7 × 7 × 7
Now, group the prime factors into triples: (3 × 3 × 3) × (5 × 5 × 5) × (7 × 7 × 7)
Each group of three identical factors gives us one factor of the cube root:
Cube root of 2460375 = 3 × 5 × 7 = 105
Thus, the cube root of 2460375 is 105.
Common Mistakes and How to Avoid Them in the Cube Root of 2460375
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 students commonly make and the ways to avoid them:
Mistake 1
Trying to find cube roots for non-perfect cube numbers by assuming they're perfect cubes.
Children might try to calculate an exact whole number for the cube root of numbers that are not perfect cubes due to incorrect assumptions.
For example, they might assume that every number will have a whole number cube root. To avoid this error, verify whether a number is a perfect cube before attempting to find a whole number cube root. For 2460375, it is indeed a perfect cube, resulting in a cube root of 105.
Cube Root of 2460375 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 2460375 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛2460375 = 105 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 exactly 105 units.
Problem 2
A company manufactures 2460375 cubic meters of material. Calculate the amount of material left after using 500000 cubic meters.
The amount of material left is 1960375 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 2460375 - 500000 = 1960375 cubic meters.
Problem 3
A tank holds 2460375 cubic meters of water. Another tank holds a volume of 530000 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 2990375 cubic meters.
Explanation
Explanation: Let’s add the volume of both tanks: 2460375 + 530000 = 2990375 cubic meters.
Problem 4
When the cube root of 2460375 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 105 = 210 The cube of 210 = 9261000
Explanation
When we multiply the cube root of 2460375 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(4000000 + 460375).
∛(4000000 + 460375) = ∛4460375 ≈ 163.353
Explanation
As shown in the question ∛(4000000 + 460375), we simplify by adding them: 4000000 + 460375 = 4460375. Then we use this step: ∛4460375 ≈ 163.353 to get the answer.
FAQs on 2460375 Cube Root
1.Can we find the Cube Root of 2460375?
2.Why is the Cube Root of 2460375 rational?
3.Is it possible to get the cube root of 2460375 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 Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Cube Root of 2460375?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube Root of 2460375?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube Root of 2460375
- 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, 105 × 105 × 105 = 2460375, therefore, 2460375 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, which is expressed as (∛).
- Rational number: A number that can be expressed as a fraction or whole number. For example, the cube root of 2460375 is rational because it is 105, a whole number.
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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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