309 LearnersLast updated on May 26th, 2025
Cube Root of 72
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.
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.
Mistake 1
For ∛72, students can make error in the important part of prime factorization.
Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair).
Mistake 2
Applying exponent rules incorrectly when finding cube roots.
∛72 is not same as 723. ∛72 = 4.16… and 723 is something very large quantity.
Mistake 3
For large non-perfect cubes, students frequently estimate wrongly and leave it with a wrong result.
Keep the methods of finding cube roots in front whenever attempting large non-perfect cubes.
Mistake 4
Students typically rely on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complex problems. So understanding the methods of finding cube roots is advisable.
Mistake 5
Misapply the cube root property like when asked to solve ∛(72)3, students might do as ∛(72×3)
Clear the concepts again and again if they don’t understand, where to do what. ∛(72)3≠∛(72×3). ∛(72)3= 72
Cube Root of 72 Examples
Problem 1
Find ∛64/ ∛72
∛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.
Problem 2
If y = ∛72, find y³
y=∛72
⇒ y3= (∛72)3
⇒ y3= 72
Answer: 72
Explanation
(∛72)3=(721/3)3=72. Using this, we found the value of y3.
Problem 3
Subtract ∛72 - ∛70
∛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.
Problem 4
What is ∛(72⁶) ?
∛(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.
Problem 5
Find ∛(72-8)
∛(72-8)
= ∛64
=4
Answer: 4
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 72 Cube Root
1. Is 72 a perfect cube or not?
2.Where is the cube root of 72?
3.What will be the cube of 72?
4.Is 72 a perfect square?
5.What are the factors of 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.
