Last updated on May 26th, 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.
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 β72 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (72)β
. If “m” is the cube root of 72, then, m3=72. Let us find the value of “m”.
We can find cube roots of 72 through a method, named as, Halley’s Method. Let us see how it finds the result.
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 βa≅ 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. β72≅ 4((43+2×72) / (2(4)3+72)) = 4.16…
Hence, 4.16… is the approximate cubic root of 72.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Find β64/ β72
β64/ β72
= 4 / 4.16
=0.962
Answer: 0.962
We know that the cubic root of 64 is 4, hence dividing 4 by β72.
If y = β72, find yΒ³
y=β72
⇒ y3= (β72)3
⇒ y3= 72
Answer: 72
(β72)3=(721/3)3=72. Using this, we found the value of y3.
Subtract β72 - β70
β72-β70
= 4.16-4.12
= 0.04
Answer: 0.04
We found the cube root of 70 and then subtracted it from the cube root of 72.
What is β(72βΆ) ?
β(726)
= ((72)6))1/3
=( 72)2
= 5184
Answer: 5184
We solved and simplified the exponent part first using the fact that, β72=(72)β
, then solved.
Find β(72-8)
β(72-8)
= β64
=4
Answer: 4
Simplified the expression, and found out the cubic root of the result.
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
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.
: He loves to play the quiz with kids through algebra to make kids love it.