357 LearnersLast updated on May 26th, 2025
Cube Root of 125
The cube root of 125 is the value “y” such that the number “y” is multiplied 3 thrice by itself. ∛ is the symbol used to denote the cube root of a number. Cube roots are used in designing loudspeakers or in pharmacology for correct dosage of medicine as per body weight.
What Is the Cube Root of 125?
The cube root of 125 is 5. The cube root of 125 is expressed as ∛125 in radical form, where the “∛" sign is called the “radical” sign. In exponential form, it is written as (125)⅓
Finding the Cube Root of 125
We can find the cube root of 125 through various methods.
- Prime Factorization method
- Subtraction method
Cube Root of 125 By Prime Factorization
Finding a cube root of 125 through the Prime Factorization method involves determining the factor of 125.
Step 1: Find the prime factors of 125.
So, 125 = 5x5x5
Step 2: Group the factors of 125 in a group of 3.
Step 3: Since 125 is a perfect cube, we have a pair of 3, so there is no need to expand it further.
The cube root of 125 can be written as ∛125 = ∛5x5x5 = 5
Therefore, the cube root of 125 is 5.
Cube Root of 125 By Subtraction Method
In this method, from the given cube number, 1, 7, 19, 37, 61, 91, 127, 169... are successively subtracted till we get zero. The number of times subtraction was performed gives the cube root of the given number.
Step 1: Subtract the 1st odd number : 125 - 1 = 124
Step 2: Subtract the next odd number: 124 - 7 = 117
Step 3: Subtract the next odd number: 117 - 19 = 98
Step 4: Subtract the next odd number: 98 - 37 = 61
Step 5: Subtract the next odd number: 61 - 61 = 0
Here the subtraction took place five times to reach zero.
Hence the cube root of 125 is 5.
Common Mistakes and How to Avoid Them in the Cube Root of 125
While finding the cube root of 125, there are some common mistakes that we often make. So let’s discuss a few of the mistakes and their solutions.
Mistake 1
Ignoring negative cube root
While calculating the cube roots, the students fail to consider the negative roots of the number.
For example, (-5)3 = -125
Cube Root of 125 Examples
Problem 1
A cube-shaped container has a volume of 125 cubic cm. What is the length of one side of the container?
5 centimeters.
Explanation
The cube root of 125 is 5, so the length of one side is 5 cm.
Problem 2
Find the value of x in the equation: x³ = 125
x = 5
Explanation
the cube root of 125 is 5.
Problem 3
Simplify the expression: √(125)
5 * √5.
Explanation
√(125) can be written as √(5³) = 53/2
Problem 4
A spherical ball has a volume of 125 cubic inches. What is the radius of the ball (to the nearest inch)?
3 inches.
Explanation
The volume of a sphere is (4/3)πr³. Setting this equal to 125 and solving for r, we find that r = 3 inches.
Problem 5
A cube-shaped box has a surface area of 150 square units. What is the volume of the box?
125 cubic units.
Explanation
First, find the side length of the cube. The surface area of a cube is 6s². Solving for s, we get s = 5.
Then, the volume is s³, which is 125 cubic units.
Conclusion
We get a cube root of a number when multiplied by itself three times. Methods like Prime Factorization, and subtraction methods are useful in finding the cube root of a perfect cube. Since we have found the cube root of 125 using all these methods, it has become quite simple to find the cube roots of any other number.
FAQs on 125 Cube Root
1.Cube root of 125?
2.Is 125 a perfect cube?
3.What is the cube root of -125?
4.Is the cube root of 125 a rational number?
5.Is there any shortcut to find the cube of any number?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube Root of 125?
8.How do technology and digital tools in Bahrain support learning Algebra and Cube Root of 125?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for Cube Root of 125
- Perfect cube: Perfect cube is the number that can be expressed as the cube of an integer.
As 125 = 5x5x5, it is a perfect cube
- Radical form:It’s the notation used to represent roots, ∛125
- Exponent form:It’s the notation used to represent roots using exponents, (125)⅓
- Equation:It is a mathematical expression that asserts the quality of two expressions.
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About BrightChamps in Bahrain
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.
