113 LearnersLast updated on May 26th, 2025
Cube Root of 210125
A number we multiply by itself three times to get the original number is its cube root. Understanding cube roots is essential in calculating volumes of cube-shaped objects and designing structures. We will now find the cube root of 210125 and explain the methods used.
What is the Cube Root of 210125?
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, ∛210125 is written as 210125(1/3). The cube root is the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 210125, then y3 can be 210125. The cube root of 210125 is an exact whole number, which is 59.
Finding the Cube Root of 210125
Finding the cube root of a number is identifying the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of 210125. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 210125 is a perfect cube, we can use the prime factorization method to find its cube root.
Cube Root of 210125 by Prime Factorization
Let's find the cube root of 210125 using the prime factorization method.
First, factorize 210125 into its prime factors: 210125 = 5 × 5 × 5 × 7 × 7 × 7
Group the prime factors in triples: (5 × 5 × 5) and (7 × 7 × 7)
The cube root is the product of one factor from each group: ∛210125 = 5 × 7 = 35
The cube root of 210125 is 35.
Common Mistakes and How to Avoid Them in the Cube Root of 210125
Finding the cube root of a number without errors can be challenging for students. Here are a few mistakes students commonly make and how to avoid them:
Mistake 1
Trying to find cube roots for numbers that aren't perfect cubes.
Students might try to calculate an exact whole number for the cube root of numbers that are not perfect cubes.
For example, they might expect a whole number result for non-perfect cubes. To avoid this error, remember that some numbers do not have a perfect cube root, unlike 210125, which is a perfect cube.
Cube Root of 210125 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of 210125 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛210125 = 59 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 59 units.
Problem 2
A company produces 210125 cubic meters of material. Calculate the amount of material used if 1000 cubic meters remain.
The amount of material used is 209125 cubic meters.
Explanation
To find the used material, we need to subtract the remaining material from the total amount:
210125 - 1000 = 209125 cubic meters.
Problem 3
A container holds 210125 cubic meters of volume. Another container holds a volume of 125 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 210250 cubic meters.
Explanation
Let’s add the volume of both containers:
210125 + 125 = 210250 cubic meters.
Problem 4
When the cube root of 210125 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 59 = 118 The cube of 118 = 1643032
Explanation
When we multiply the cube root of 210125 by 2, it results in a significant increase in volume because the cube value increases exponentially.
Problem 5
Find ∛(105062 + 105063).
∛(105062 + 105063) = ∛210125 = 59
Explanation
As shown in the question ∛(105062 + 105063), we can simplify that by adding them.
So, 105062 + 105063 = 210125.
Then we use this step: ∛210125 = 59 to get the answer.
FAQs on 210125 Cube Root
1.Can we find the Cube Root of 210125?
2.Why is the Cube Root of 210125 rational?
3.Is it possible to get the cube root of 210125 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 States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube Root of 210125?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 210125?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 210125
- 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, 35 × 35 × 35 = 210125, therefore, 210125 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 210125(1/3), ⅓ is the exponent, which denotes the cube root of 210125.
- Radical sign: The symbol used to represent a root, which is expressed as (∛).
- Rational number: Numbers that can be expressed as a fraction of two integers. The cube root of 210125 is rational because it equals 59.
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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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