Cube Root of 125
2026-02-28 11:52 Diff

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Last updated on August 5, 2025

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. 
 

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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. 

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Problem 1

A cube-shaped container has a volume of 125 cubic cm. What is the length of one side of the container?

Okay, lets begin

5 centimeters.
 

Explanation

The cube root of 125 is 5, so the length of one side is 5 cm.

Well explained 👍

Problem 2

Find the value of x in the equation: x³ = 125

Okay, lets begin

x = 5
 

Explanation

the cube root of 125 is 5.

Well explained 👍

Problem 3

Simplify the expression: √(125)

Okay, lets begin

 5 * √5.
 

Explanation

 √(125) can be written as √(5³) = 53/2
 

Well explained 👍

Problem 4

A spherical ball has a volume of 125 cubic inches. What is the radius of the ball (to the nearest inch)?

Okay, lets begin

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. 
 

Well explained 👍

Problem 5

A cube-shaped box has a surface area of 150 square units. What is the volume of the box?

Okay, lets begin

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.
 

Well explained 👍

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?

125 is a perfect cube because it can as 5x5x5

3.What is the cube root of -125?

 Cube root of -125 will be -5.
 

4.Is the cube root of 125 a rational number?

5.Is there any shortcut to find the cube of any number?

There is no shortcut to find the cube root of any number. The best way to go is with the prescribed and standard methods. 
 

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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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.

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: He loves to play the quiz with kids through algebra to make kids love it.