152 LearnersLast updated on May 26th, 2025
Cube Root of 8615125
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 8615125 and explain the methods used.
What is the Cube Root of 8615125?
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, ∛8615125 is written as 8615125(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 8615125, then y3 can be 8615125. Since 8615125 is a perfect cube, its cube root is exactly 205.
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Finding the Cube Root of 8615125
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 8615125. 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 like 8615125, we can use the prime factorization method for an exact result.
Cube Root of 8615125 by Prime Factorization
Let's find the cube root of 8615125 using the prime factorization method:
1. Break down 8615125 into its prime factors: \(8615125 = 5^3 \times 7^3 \times 11^3\).
2. Since each factor is raised to the power of 3, the cube root can be directly obtained by taking one of each factor: - (∛(5^3) = 5) - (∛(7^3) = 7) - (∛(11^3) = 11)
3. Multiply these results: (5 times 7 times 11 = 385).
The cube root of 8615125 is 205.
Common Mistakes and How to Avoid Them in the Cube Root of 8615125
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 may attempt to calculate an exact whole number for the cube root of numbers that are not perfect cubes. However, 8615125 is a perfect cube, so its cube root is exactly 205. To avoid this error, determine if the number is a perfect cube first.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that a cube root can also be written in exponent form.
For example: Forgetting that the cube root of 8615125 is \(8615125^{1/3}\). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
Students might mistakenly assume that finding the cube root of 8615125 involves dividing it by 3. To avoid this, remember that the cube root of 8615125 is the number that when multiplied by itself three times equals 8615125.
Mistake 4
Using inappropriate methods for perfect cubes
Instead of using the prime factorization method for perfect cubes, students might use approximation or other methods. For a perfect cube like 8615125, prime factorization is the most straightforward method.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps.
For example: rounding an intermediate result before the calculation is complete. To avoid this, ensure the whole calculation is done, then round the final result if necessary.
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Cube Root of 8615125 Examples:
Problem 1
Imagine you have a cube-shaped container with a total volume of 8615125 cubic centimeters. Find the length of one side of the container.
Side of the cube = ∛8615125 = 205 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 205 units.
Problem 2
A factory produces 8615125 cubic meters of a product. Calculate the remaining product after using 1000000 cubic meters.
The remaining product is 7615125 cubic meters.
Explanation
To find the remaining product, subtract the used product from the total amount:
8615125 - 1000000 = 7615125 cubic meters.
Problem 3
A storage unit has a volume of 8615125 cubic meters. Another unit has a volume of 500000 cubic meters. What would be the total volume if the units are combined?
The total volume of the combined units is 9115125 cubic meters.
Explanation
Add the volume of both units:
8615125 + 500000 = 9115125 cubic meters.
Problem 4
When the cube root of 8615125 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 205 = 615
The cube of 615 = 231344375
Explanation
Multiplying the cube root of 8615125 by 3 results in a significant increase in the volume when the cube of the new value is calculated.
Problem 5
Find ∛(8615125 + 8615125).
∛(8615125 + 8615125) = ∛17230250 ≈ 259.5
Explanation
As shown in the question ∛(8615125 + 8615125), we first add the numbers:
8615125 + 8615125 = 17230250.
Then we use this step: ∛17230250 ≈ 259.5 to get the answer.
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FAQs on Cube Root of 8615125
1.Can we find the Cube Root of 8615125?
2.Why is Cube Root of 8615125 rational?
3.Is it possible to get the cube root of 8615125 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 Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube Root of 8615125?
8.How do technology and digital tools in Singapore support learning Algebra and Cube Root of 8615125?
9.Does learning Algebra support future career opportunities for students in Singapore?
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Important Glossaries for Cube Root of 8615125
- 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: \(5 \times 5 \times 5 = 125\), therefore, 125 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (8615125^{1/3}), ⅓ is the exponent which denotes the cube root of 8615125.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Rational number: A number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. The cube root of 8615125 is 205, which is a rational number because it can be expressed as a fraction (205/1).
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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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