Cube Root of 72
2026-02-28 23:35 Diff
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Last updated on August 5, 2025

We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 72, and its examples.

What Is the Cube Root of 72?

The cube root of 72 is the value which, when multiplied by itself three times (cubed), gives the original number 72. The cube root of 72 is 4.1601676461.  The cube root of 72 is expressed as ∛72 in radical form, where the “ ∛ ”  sign” is called the “radical” sign. In exponential form, it is written as (72)⅓. If “m” is the cube root of 72, then, m3=72. Let us find the value of “m”.
 

Finding the Cube Root of 72

We can find cube roots of 72 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 72 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 72.


Step 1: Let a=72. Let us take x as 4, since 43=64 is the nearest perfect cube which is less than 72.


Step 2: Apply the formula.  ∛72≅ 4((43+2×72) / (2(4)3+72)) = 4.16…


Hence, 4.16… is the approximate cubic root of 72.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 72

Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.

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Problem 1

Find ∛64/ ∛72

Okay, lets begin

 ∛64/ ∛72

= 4 / 4.16

=0.962


Answer: 0.962
 

Explanation

We know that the cubic root of 64 is 4, hence dividing 4 by  ∛72.
 

Well explained 👍

Problem 2

If y = ∛72, find y³

Okay, lets begin

 y=∛72


⇒ y3= (∛72)3 


⇒ y3= 72


Answer: 72
 

Explanation

(∛72)3=(721/3)3=72. Using this, we found the value of y3.

Well explained 👍

Problem 3

Subtract ∛72 - ∛70

Okay, lets begin

∛72-∛70

= 4.16-4.12

= 0.04


Answer:  0.04
 

Explanation

We found the cube root of 70 and then subtracted it from the cube root of 72.
 

Well explained 👍

Problem 4

What is ∛(72⁶) ?

Okay, lets begin

 ∛(726)

= ((72)6))1/3

=( 72)2

= 5184


Answer: 5184 
 

Explanation

We solved and simplified the exponent part first using the fact that, ∛72=(72)⅓, then solved.
 

Well explained 👍

Problem 5

Find ∛(72-8)

Okay, lets begin

 ∛(72-8)

= ∛64

=4


Answer: 4
 

Explanation

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

Well explained 👍

FAQs on 72 Cube Root

1. Is 72 a perfect cube or not?

 72 is not a perfect cube, since on prime factorization of 72, we get,  ∛72 =  ∛(3×3×2×2×2) = 2∛9. We see here that we can get only a set of 2 in the power of 3, but 9 is remaining.
 

2.Where is the cube root of 72?

The cube root value of 72 is 4.1601676461. This value lies between 4 and 5 in the number line. To be more precise, this value lies between 4 and 4.2.
 

3.What will be the cube of 72?

The cube of 72 is obtained when we multiply 72 with itself for 3 times. It is 373248.
 

4.Is 72 a perfect square?

 72 is not a perfect square since, on prime factorization of 72 we obtain, √72 =  √(3×3×2×2×2) = 6√2. This clearly proves that 72 is not a perfect square.
 

5.What are the factors of 72?

Factors are dividers which divide 72 perfectly, leaving 0 remainder, and so for 72, factors are:

1,2,3,4,6,8,9,12,18,24,36,72.
 

Important Glossaries for Cube Root of 72

  • Cube root properties - The features when cube root is applied to any number. Those are: 1) The cube root of all odd numbers is an odd number. The same applies for even numbers also, that is, the cube of any even number is even. 
  •  

2) The cube root of a negative number is also negative.


3) If the cube root of a number is a whole number, then that original number is said to be perfect cube

  • Irrational Numbers - Numbers which cannot be expressed as m/n form, where m and n are integers and n not equal to 0, are called Irrational numbers.
  • Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be found out.
  • 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 near to the correct answer, but not perfectly correct.
  • Iterative method - This method is a mathematical process which uses an initial value to generate a further sequence of solutions for a problem, step-by-step. 
     

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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.