Cube Root of 25
2026-02-28 10:18 Diff
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Last updated on August 5, 2025

The cube root of 25 is the value which, when multiplied by itself three times (cubed), gives the original number 25. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, creating unique digital art etc.

What Is the Cube Root of 25?

The cube root of 25 is 2.92401773821. The cube root of 25 is expressed as ∛25 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (25)1/3.  If “m” is the cube root of 25, then, m3=25.  Let us find the value of “m”.
 

Finding the Cube Root of 25

The Prime Factorization of 25 is 5×5, so, the cube root of 25 is expressed as ∛25 as its simplest radical form. We can find the cube root of 25 through a method, named Halley’s Method. Let us see how it finds the result.
 

Cube Root of 25 By Halley’s Method

Now, what is Halley’s Method?

It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.


Formula is ∛a≅ x((x3+2a) / (2x3+a)), where 


a=given number whose cube root you are going to find


x=integer guess for the cubic root


Let us apply Halley’s method on the given number 25.


Step 1: Let a=25. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 25.


Step 2: Apply the formula.  ∛25≅ 2((23+2×25) / (2(2)3+25))= 2.82…


Hence, 2.82… is the approximate cubic root of 25.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 25

some common mistakes with their solutions are given below:

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Problem 1

Find ∛25/ ∛14

Okay, lets begin

 ∛25/ ∛14

= 2.924 / 2.410

= 2924/2410

=1.213


Answer: 1.213
 

Explanation

We found that the cubic root of 14 is 2.410…, hence dividing  ∛25 by ∛14.
  

Well explained 👍

Problem 2

The Volume of a cube is 25 cubic centimeters, find the length of one side of the cube.

Okay, lets begin

We know that, (side of a cube)3 = Volume of a cube


⇒side of the cube =  ∛(Volume of the cube)


⇒side of the cube = ∛25


⇒ side of the cube = 2.924 cm


Answer: 2.924 cm
 

Explanation

We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
 

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Problem 3

Subtract ∛25 - ∛8, ∛27-∛25

Okay, lets begin

∛25-∛8

= 2.924–2

=0.924


∛27-∛25

= 3-2.924

= 0.076


Answer:  0.924, 0.076
 

Explanation

We know that the cubic root of 8 is 2, hence subtracting  ∛8 from ∛25. Applying the same for the next one, we know that the cubic root of 27 is 3, hence subtracting ∛25 from ∛27.
 

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Problem 4

What is ∛(25²) ?

Okay, lets begin

 ∛(252)

= ∛625

= 8.549…

 
Answer: 8.549… 
 

Explanation

We first found the square value of 25, which is 625, and then found out the cube root of 625.
 

Well explained 👍

Problem 5

Find ∛((25+2)×(25+39)).

Okay, lets begin

 ∛((25+2)×(25+39))

= ∛(27×64)

=∛1728

= 12


Answer: 12
 

Explanation

Simplified the expression, and found out the cubic root of the result. 
 

Well explained 👍

FAQs on 25 Cube Root

1.What does 3√27 mean ?

3√27 = 3√(3×3×3) = 3×3√3 =9√3.
 

2.Is 25 a perfect cube?

No, 25 is not a perfect cube, since, ∛25=2.92401773821, which is not a whole number and irrational too.
 

3.What is 25 cubes?

4.How to find cube roots?

The cube root of a number is the value which, when multiplied by itself three times (cubed), gives the original number. So, cube roots can be found through prime factorization method or Halley’s method.
 

5.Is 45 a perfect cube?

No, 45 is not a perfect cube, since, ∛45=3.55689330449, which is not a whole number, and it is irrational too.
 

Important Glossaries for Cube Root of 25

  • Irrational Numbers - Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 
  • Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. These cannot be in fractional or decimal form. 
  • Square root -The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.
  • Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
  • Approximation - Finding out a value which is nearly correct, but not perfectly correct, as if the approximate value is just near and close the original value.
  • Iterative method - This method is a process, used in mathematics, which uses an initial value to generate further and step-by-step sequence of solutions for a problem.
     

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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.