118 LearnersLast updated on May 26th, 2025
Cube Root of 614125
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 614125 and explain the methods used.
What is the Cube Root of 614125?
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, ∛614125 is written as 614125(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 614125, then y3 can be 614125. Since the cube root of 614125 is an exact value, we can write it as exactly 85.
Finding the Cube Root of 614125
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 614125. 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 614125 is a perfect cube, we can use this method.
Cube Root of 614125 by Prime Factorization Method
Let's find the cube root of 614125 using the prime factorization method.
First, we find the prime factors of 614125: 614125 = 5 × 5 × 5 × 7 × 7 × 7.
Grouping the factors into triples, we have (5 × 5 × 5) and (7 × 7 × 7).
The cube root is the product of one factor from each group: ∛614125 = 5 × 7 = 35.
The cube root of 614125 is 85.
Common Mistakes and How to Avoid Them in the Cube Root of 614125
Finding the perfect cube of a number without any errors can be a difficult task for the 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 cube roots for non-perfect cube numbers.
Children always try to calculate an exact whole number for the cube root of numbers that are not perfect cubes. However, 614125 is a perfect cube, so it has an exact cube root of 85. To avoid confusion, ensure the number is a perfect cube before attempting to find an exact cube root.
Cube Root of 614125 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of 614125 cubic centimeters. Find the length of one side of the box, which is equal to its cube root.
Side of the cube = ∛614125 = 85 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 85 units.
Problem 2
A company manufactures 614125 cubic meters of material. Calculate the amount of material left after using 125 cubic meters.
The amount of material left is 614000 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 614125 - 125 = 614000 cubic meters.
Problem 3
A container holds 614125 cubic liters of liquid. Another container holds a volume of 2000 cubic liters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 616125 cubic liters.
Explanation
Explanation: Let’s add the volume of both containers: 614125 + 2000 = 616125 cubic liters.
Problem 4
When the cube root of 614125 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 85 = 170 The cube of 170 = 4913000
Explanation
When we multiply the cube root of 614125 by 2, it results in a significantly larger volume, as the cube of the new value increases exponentially.
Problem 5
Find ∛(500000 + 114125).
∛(500000 + 114125) = ∛614125 = 85
Explanation
As shown in the question ∛(500000 + 114125), we can simplify that by adding them.
So, 500000 + 114125 = 614125.
Then we use this step: ∛614125 = 85 to get the answer.
FAQs on 614125 Cube Root
1.Can we find the Cube Root of 614125?
2.Why is the Cube Root of 614125 not irrational?
3.Is it possible to get the cube root of 614125 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 614125?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube Root of 614125?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for Cube Root of 614125
- 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 × 5 × 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 614125(1/3), ⅓ is the exponent which denotes the cube root of 614125.
- Radical sign: The symbol used to represent a root is expressed as (∛).
- Factorization: The process of breaking down a number into its prime components. For example, 614125 can be broken down into 5 × 5 × 5 × 7 × 7 × 7.
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About BrightChamps in United Arab Emirates
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.
