Table Of Contents
100 LearnersLast updated on April 28th, 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
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.
Explanation
Problem 2
A company produces 210125 cubic meters of material. Calculate the amount of material used if 1000 cubic meters remain.
Explanation
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?
Explanation
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?
Explanation
Problem 5
Find ∛(105062 + 105063).
Explanation
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?
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.
Explore More algebra
Previous to Cube Root of 210125
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.
