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295 LearnersLast updated on November 30th, 2024
Cubic Root of 36
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 β36 in radical form, where the β β β sign is called the βradicalβ sign. In exponential form, it is written as (36)β
. If βmβ is the cube root of 36, then, m3=36. Let us find the value of βmβ.
Finding the Cube Root of 36
The cube root of 36 is expressed as β36 as its simplest radical form,
since 36 = 2Γ2Γ3Γ3
β36 = β(2Γ2Γ3Γ3)
Group together three same factors at a time and put the remaining factor under the β .
β36= β36
We can find cube root of 36 through a method, named as, Halleyβs Method. Let us see how it finds the result.
Cube Root of 36 By Halleyβs Method
Now, what is Halleyβs 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 βxβ.
Formula is βaβ
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 Halleyβs 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. β36β
3((33+2Γ36) / (2(3)3+36))= 3.3
Hence, 3.3 is the approximate cubic root of 36.
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 β216, the student might mistakenly think the answer is 5, where 63
Donβt round off to the nearest number and find cube roots, it is advisable to use proper methods to find cube roots.
Cube Root of 36 Examples
Problem 1
Find (β32/ β36) Γ (β33/ β36) Γ (β34/ β36)
(β32/ β36) Γ (β33/ β36) Γ (β34/ β16)
= (β32Γ β33Γ β34) / (β36Γ β36Γ β36)
=(β32Γ β33Γ β34)/ ((36)β
)3
=(β32Γ β33Γ β34)/36
=(3.174 Γ 3.207 Γ 3.239)/36
Answer: (3.174 Γ 3.207 Γ 3.239)/36
Explanation
We used the fact that ((36)β
)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 Γ breadth Γ height = 4 Γ 3 Γ 3.5 cubic units = 42 cubic units.
Given, Volume of a cube = 36 cubic units
β side Γ side Γ side = 36 cubic units
β side = β36
β 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 β36 Γ β125
β36Γβ125
= 3.301Γ5
= 16.505
Answer: 16.505
Explanation
We know that the cubic root of 125 is 5, hence multiplying β125 with β36.
Problem 4
What is β(36^6Γ1/6) ?
β(366Γ1/6)
= (36)1/3
= 3.301β¦
Answer: 3.301
Explanation
We solved and simplified the exponent part first using the fact that, (366Γ1/6)=36, then solved.
Problem 5
Find β(36-(-28)).
β(36-(-28))
= β(36+28)
=β64=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 β ?
2.How to find β36 ?
3.What does β mean?
4.Is 27 a perfect cube?
5.Is β9 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 βyβ such that when βyβ is multiplied by itself β y Γ y, the result is the original number.
- Polynomial: It is an algebraic expression made up of variables like βxβ 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.
