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821 LearnersLast updated on August 5, 2025
Cubic Root of 36
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.
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Common Mistakes and How to Avoid Them in the Cube Root of 36
some common mistakes with their solution are given below:
Mistake 1
Students might guess the cube root by rounding to the nearest number, leading to inaccuracy. For ∛216, the student might mistakenly think the answer is 5, where 63
Don’t round off to the nearest number and find cube roots, it is advisable to use proper methods to find cube roots.
Mistake 2
Confusing or misidentifying prime numbers with composite numbers while performing prime factorization to find cube roots.
While prime factorization, make sure you know which numbers are prime and which are not.
Mistake 3
Applying exponent rules incorrectly when finding cube roots.
∛36 is not same as 363. ∛36 = 3.301… and 363=46656.
Mistake 4
Students often 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
Not checking for perfect cubes, like that of 27, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 100.
Cube Root of 36 Examples
Problem 1
Find (∛32/ ∛36) × (∛33/ ∛36) × (∛34/ ∛36)
(∛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.
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.
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.
Problem 3
Multiply ∛36 × ∛125
∛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.
Problem 4
What is ∛(36^6×1/6) ?
∛(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.
Problem 5
Find ∛(36-(-28)).
∛(36-(-28))
= ∛(36+28)
=∛64=4
Answer: 4
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 36 Cube Root
1.How to calculate ∛ ?
2.How to find √36 ?
3.What does ∛ mean?
4.Is 27 a perfect cube?
5.Is √9 equals 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.
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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.
