102 LearnersLast updated on May 26th, 2025
Cube Root of 3125
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 3125 and explain the methods used.
What is the Cube Root of 3125?
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, ∛3125 is written as 3125(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 3125, then y³ can be 3125. Since 3125 is a perfect cube, its cube root is exactly 15.
Finding the Cube Root of 3125
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 3125. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Estimation method
- Subtraction method
- Halley’s method
Since 3125 is a perfect cube, we can use the prime factorization method efficiently.
Cube Root of 3125 by Prime Factorization
Let's find the cube root of 3125 using the prime factorization method.
First, perform the prime factorization of 3125: 3125 = 5 × 5 × 5 × 5 × 5
Grouping the factors into triples gives us: (5 × 5 × 5) = 125, and (5 × 5) = 25
Since 3125 is the cube of 5 (i.e., 5³), we take one factor from each group: ∛3125 = 5
The cube root of 3125 is 15.
Common Mistakes and How to Avoid Them in the Cube Root of 3125
Finding the perfect cube of a number without any errors can be a difficult task. This happens for many reasons. Here are a few mistakes commonly made and ways to avoid them:
Mistake 1
Trying to find a non-perfect cube root for perfect cube numbers.
Sometimes people mistakenly look for an approximate value for numbers like 3125, assuming it's not a perfect cube. To avoid this, remember that if the number can be expressed as a product of a number multiplied by itself three times, it is a perfect cube.
Cube Root of 3125 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 3125 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛3125 = 15 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 15 units.
Problem 2
A company manufactures 3125 cubic meters of material. Calculate the amount of material left after using 500 cubic meters.
The amount of material left is 2625 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
3125 - 500 = 2625 cubic meters.
Problem 3
A bottle holds 3125 cubic meters of volume. Another bottle holds a volume of 75 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 3200 cubic meters.
Explanation
Explanation: Let’s add the volume of both bottles:
3125 + 75 = 3200 cubic meters.
Problem 4
When the cube root of 3125 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 15 = 30 The cube of 30 = 27000
Explanation
When we multiply the cube root of 3125 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(2500 + 625).
∛(2500 + 625) = ∛3125 = 15
Explanation
As shown in the question ∛(2500 + 625), we can simplify that by adding them.
So, 2500 + 625 = 3125.
Then we use this step: ∛3125 = 15 to get the answer.
FAQs on 3125 Cube Root
1.Can we find the Cube Root of 3125?
2.Why is Cube Root of 3125 rational?
3.Is it possible to get the cube root of 3125 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 3125
- 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 a(1/3), ⅓ is the exponent which denotes the cube root of 'a'.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Rational number: A number that can be expressed as a fraction of two integers is rational. For example, the cube root of 3125 is rational because it is 15.
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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.
