136 LearnersLast updated on May 26th, 2025
Cube Root of 91125
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 91125 and explain the methods used.
What is the Cube Root of 91125?
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, ∛91125 is written as (91125{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 91125, then (y3) can be 91125. The cube root of 91125 is 45.
Finding the Cube Root of 91125
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 91125. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 91125 is a perfect cube, we can use the prime factorization method to find its cube root efficiently.
Cube Root of 91125 by Prime Factorization Method
Let's find the cube root of 91125 using the prime factorization method.
First, we find the prime factors of 91125: 91125 = 3 × 3 × 3 × 5 × 5 × 5 × 11 × 11 × 11
Group the prime factors in triples: (3 × 3 × 3), (5 × 5 × 5), (11 × 11 × 11)
The cube root is the product of one factor from each group: 3 × 5 × 11 = 45
Therefore, the cube root of 91125 is 45.
Common Mistakes and How to Avoid Them in the Cube Root of 91125
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 cube roots without proper factorization.
Students may try to calculate cube roots without breaking down the number into its prime factors for perfect cubes.
For example, assuming an approximate value for 91125 without factorization. To avoid this error, ensure you know the prime factors of a number if it is a perfect cube.
Cube Root of 91125 Examples:
Problem 1
Imagine you have a cube-shaped storage box that has a total volume of 91125 cubic centimeters. Find the length of one side of the box, equal to its cube root.
Side of the cube = ∛91125 = 45 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 45 units.
Problem 2
A company manufactures 91125 cubic meters of material. Calculate the amount of material left after using 45000 cubic meters.
The amount of material left is 46125 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
91125 - 45000 = 46125 cubic meters.
Problem 3
A container holds 91125 cubic meters of volume. Another container holds a volume of 3375 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 94500 cubic meters.
Explanation
Let’s add the volume of both containers:
91125 + 3375 = 94500 cubic meters.
Problem 4
When the cube root of 91125 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 45 = 90 The cube of 90 = 729000
Explanation
When we multiply the cube root of 91125 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(45000 + 46125).
∛(45000 + 46125) = ∛91125 = 45
Explanation
As shown in the question ∛(45000 + 46125), we can simplify that by adding them.
So, 45000 + 46125 = 91125.
Then we use this step: ∛91125 = 45 to get the answer.
FAQs on 91125 Cube Root
1.Can we find the Cube Root of 91125?
2.Why is the Cube Root of 91125 rational?
3.Is it possible to get the cube root of 91125 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there a formula to find the cube root of a number?
Important Glossaries for Cube Root of 91125
- 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: 3 × 3 × 3 = 27, therefore, 27 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: The numbers that can be expressed as a fraction of two integers are rational. For example, 45 is rational because it can be expressed as 45/1.
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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.
