Cubic Root of 36
2026-02-28 08:18 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-36

815 Learners

Last updated on August 5, 2025

The cube root of 36 is the value that, when multiplied by itself three times (cubed), gives the original number 36. 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 36?

The cube root of 36 is 3.30192724889. The cube root of 36 is expressed as ∛36 in radical form, where the “ ∛ “  sign is called the “radical” sign. In exponential form, it is written as (36)⅓. If “m” is the cube root of 36, then, m3=36. Let us find the value of “m”.
 

Finding the Cube Root of 36

The cube root of 36 is expressed as ∛36 as its simplest radical form,

since 36 = 2×2×3×3


∛36 = ∛(2×2×3×3)


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


∛36= ∛36 


 We can find cube root of 36 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 36 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 36.


Step 1: Let a=36. Let us take x as 3, since, 33=27 is the nearest perfect cube which is less than 36.


Step 2: Apply the formula.  ∛36≅ 3((33+2×36) / (2(3)3+36))= 3.3


Hence, 3.3 is the approximate cubic root of 36.
 

Explore Our Programs

Common Mistakes and How to Avoid Them in the Cube Root of 36

some common mistakes with their solution are given below:

Download Worksheets

Problem 1

Find (∛32/ ∛36) × (∛33/ ∛36) × (∛34/ ∛36)

Okay, lets begin

 (∛32/ ∛36) × (∛33/ ∛36) × (∛34/ ∛16)


= (∛32× ∛33× ∛34) / (∛36× ∛36× ∛36)


=(∛32× ∛33× ∛34)/ ((36)⅓)3


=(∛32× ∛33× ∛34)/36


=(3.174 × 3.207 × 3.239)/36


Answer: (3.174 × 3.207 × 3.239)/36
 

Explanation

We used the fact that ((36)⅓)3=36 and then found the cube roots of 32,33, and 34 and simplified.
 

Well explained 👍

Problem 2

The length, breadth and height of a cuboid is 4 unit, 3 unit, and 3.5cm respectively. Find its volume, also find the measure of a side of a cube whose volume is 36 cubic units.

Okay, lets begin

Volume of a cuboid = length × breadth × height = 4 × 3 × 3.5 cubic units = 42 cubic units.


Given, Volume of a cube = 36 cubic units


⇒ side × side × side = 36 cubic units


⇒ side =  ∛36


⇒ side = 3.301 units


Answer: Volume of the cuboid = 42 cubic units


Side length of the cube = 3.301 units
 

Explanation

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

Well explained 👍

Problem 3

Multiply ∛36 × ∛125

Okay, lets begin

∛36×∛125

= 3.301×5

= 16.505


Answer:       16.505
 

Explanation

We know that the cubic root of 125 is 5, hence multiplying  ∛125 with ∛36.
 

Well explained 👍

Problem 4

What is ∛(36^6×1/6) ?

Okay, lets begin

∛(366×1/6)

= (36)1/3

= 3.301… 


Answer:        3.301 
 

Explanation

We solved and simplified the exponent part first using the fact that, (366×1/6)=36, then solved.
 

Well explained 👍

Problem 5

Find ∛(36-(-28)).

Okay, lets begin

 ∛(36-(-28))

= ∛(36+28)

=∛64=4


Answer:        4
 

Explanation

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

Well explained 👍

FAQs on 36 Cube Root

1.How to calculate ∛ ?

∛, i.e., cube root can be calculated basically like if x is a number such that x = m×m×m, then the cube root of x is ∛x = ∛(m×m×m) = m.
 

2.How to find √36 ?

3.What does ∛ mean?

 ∛ is a symbol which denotes Cube Root.

4.Is 27 a perfect cube?

Yes, 27 is a perfect cube because 27 = 3×3×3. 
 

5.Is √9 equals 3?

Yes, √9 is equal to 3 since, √9=√(3× 3)=3.
 

Important Glossaries for Cube Root of 36

  • 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.
  • 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.
     

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.