Cube Root of 24
2026-02-28 23:44 Diff
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Last updated on August 5, 2025

The cube root of 24 is the value that, when multiplied by itself three times (cubed), gives the original number 24. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.

What Is the Cube Root of 24?

The cube root of 24 is 2.88449914061. The cube root of 24 is expressed as ∛24 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (24)⅓. If “m” is the cube root of 24, then, m3=24. Let us find the value of “m”.
 

Finding the Cube Root of 24

The cube root of 24 is expressed as 2∛3 as its simplest radical form,

since 24 = 2×2×2×3


∛24 = ∛(2×2×2×3)


Group together three same factors at a time and put the remaining factor under the ∛ .


∛24= 2∛3


 We can find cube root of 24 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 24 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 24.


Step 1: Let a=24. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 24.


Step 2: Apply the formula.  ∛24≅ 2((23+2×24) / (2(2)3+24))= 2.8


Hence, 2.8 is the approximate cubic root of 24.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 24

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Problem 1

The length, breadth and height of a cuboid is 2 unit, 2.5 unit, and 2.7cm respectively. Find its volume, also find the measure of a side of a cube whose volume is 24 cubic units.

Okay, lets begin

Volume of a cuboid = length × breadth × height = 2 × 2.5 × 2.7 cubic units = 13.5 cubic units.


Given, Volume of a cube = 24 cubic units


⇒ side × side × side = 24 cubic units


⇒ side =  ∛24


⇒ side = 2.884 units


Answer: Volume of the cuboid = 13.5 cubic units


Side length of the cube = 2.884 units
 

Explanation

Applied the formula and concept of the volume of a cuboid and cube and solved.

Well explained 👍

Problem 2

If y = ∛24, find y³/ y⁶

Okay, lets begin

y=∛24


⇒ y3/y6= (∛24)3 / (∛24)6


⇒ y3/y6= 24/ (24)2= 1/24


Answer:     1/24
 

Explanation

 (∛24)3

=(241/3)3=24,

and (∛24)6=(241/3)6=(24)2.

Using this, we found the value of y3/y6.
 

Well explained 👍

Problem 3

Multiply ∛24 × ∛64 × ∛125

Okay, lets begin

∛24×∛64× ∛125

= 2.884×4×5

= 57.68 

Answer:          57.68
 

Explanation

 We know that the cubic root of 64 is 4 and that of 125 is 5, hence multiplying.
 

Well explained 👍

Problem 4

What is ∛(24⁶) ?

Okay, lets begin

∛(246)

= ((24)6))1/3

= ( 24)2

= 576

Answer:       576

Explanation

We solved and simplified the exponent part first using the fact that, ∛24=(24)⅓, then solved.
 

Well explained 👍

Problem 5

Find ∛24 / 2884.

Okay, lets begin

 (∛24) / 2884

= 2.884 /2884

= 0.001


Answer:        0.001
 

Explanation

Simplified the expression, and found out the result. 
 

Well explained 👍

FAQs on 24 Cube Root

1.What is the perfect cube near to 24?

 Perfect cube near to 24 is 27 is the cube of 3.
 

2.How to solve √24 ?

√24 = √(2×2×2×3) = 2×√(2 ×3)= 2√6.
 

3.How to find cube root?

Cube root of a number can be found through Prime factorization, and more precisely through Halley’s Method. 
 

4.What is √24 simplified?

The simplified form is → √24 = √(2×2×2×3) = 2×√(2 ×3)= 2√6.
 

5.Is 24 a perfect root?

Important Glossaries for Cube Root of 24

  • Integers: Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.
  • Whole numbers: The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. 
  • Square root : The square root of a number is a value “y” such that when “y” is multiplied by itself → y × y, the result is the original number.
  • PolynomiaI: 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.
  • Iterative method:This method is a mathematical process 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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