Cube Root of 4
2026-02-28 10:57 Diff
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Last updated on August 5, 2025

The cube root of 4 is the value that, when multiplied by itself three times (cubed), gives the original number 4. 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 4?

The cube root of 4 is 1.58740105197. The cube root of 4 is expressed as ∛4 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (4)⅓.  If “m” is the cube root of 4, then, m3=4.  Let us find the value of “m”.
 

Finding the Cube Root of 4

The cube root of 4 is expressed as ∛4 as its simplest radical form,

since 4 = 2×2


∛4 = ∛(2×2)


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


∛4= ∛4 


 We can find cube root of 4 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 4 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 4.


Step 1: Let a=4. Let us take x as 1, since, 13=1 is the nearest perfect cube which is less than 4.


Step 2: Apply the formula.  ∛4≅ 1((13+2×4) / (2(1)3+4))= 1.5


Hence, 1.5 is the approximate cubic root of 4.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 4

some common mistakes with their solutions are given below:

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Problem 1

Find ∛4/ ∛6

Okay, lets begin

  ∛4/ ∛6

= 1.587 / 1.817

= 1587/1817

= 0.873


Answer:     0.873
 

Explanation

We know that the cubic root of 6 is 1.817, hence dividing  ∛4 by ∛6.
 

Well explained 👍

Problem 2

The Volume of a cube is 4 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 = ∛4


⇒ side of the cube = 1.587 cm


Answer:      1.587 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 ∛4 - ∛8

Okay, lets begin

∛4-∛8

= 1.587–2

= -0.413


Answer:      -0.413
 

Explanation

We know that the cubic root of 8 is 2, hence subtracting  ∛8 from ∛4.
 

Well explained 👍

Problem 4

What is ∛(4²) ?

Okay, lets begin

 ∛(42)

= ∛16

= 2.519… 

Answer:     2.519… 
 

Explanation

We first found the square value of 4, which is 16, and then found out the cube root of 16.

Well explained 👍

Problem 5

Find ∛(4+4).

Okay, lets begin

∛(4+4)

= ∛8

= 2


Answer:      2
 

Explanation

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

Well explained 👍

FAQs on Cube Root of 4

1.How to solve 3√4 ?

2.How do you calculate cube root?

We can calculate cube root through methods like prime factorization and Halley’s method.
 

3.What will be the cube of 4?

4.How to solve 3√2 ?

3√2 cannot be solved further because it is already in the simplest radical form. However, we can find out the value of √2 and multiply it with 3.
 

5.How to solve cube root of 5?

The cube root of 5 can be solved through Halley’s method in a most easy way. The value is 1.7099.
 

Important Glossaries for Cube Root of 4

  • Integers: Integers are numbers that can be positive, negative, or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. The examples of integers are, 1, 2, 5,8, -9, -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, which, on multiplication by itself, gives the original number.
  • 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.
  • 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.

Fun Fact

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