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685 LearnersLast updated on August 5, 2025
Cube Root of 243
What Is the Cube Root of 243?
The cube root of 243 is 6.24025146916. The cube root of 243 is expressed as ∛243 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (243)1/3. If “m” is the cube root of 243, then, m3=243. Let us find the value of “m”.
Finding the Cube Root of 243
The cube root of 243 is expressed as 3∛9 as its simplest radical form, since
243 = 3×3×3×3×3
∛243 = ∛(3×3×3×3×3)
Group together three same factors at a time and put the remaining factor under ∛ .
∛243= 3∛9
We can find cube root of 243 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 243 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 243.
Step 1: Let a=243. Let us take x as 6, since, 63=216 is the nearest perfect cube which is less than 243.
Step 2: Apply the formula. ∛243≅ 6((63+2×243) / (2(6)3+243))= 6.24
Hence, 6.24 is the approximate cubic root of 243.
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Common Mistakes and How to Avoid Them in the Cube Root of 243
some common mistakes and solutions 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.
∛243 is not same as 2433. ∛243 = 6.24… and 2433=14348907.
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 216, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from1 to 300.
Cube Root of 243 Examples
Problem 1
Find (∛240/ ∛243) × (∛241/ ∛243) × (∛242/ ∛243)
(∛240/ ∛243) × (∛241/ ∛243) × (∛242/ ∛243)
= (∛240× ∛241× ∛242) / (∛243× ∛243× ∛243)
=(∛240× ∛241× ∛242)/ ((243)⅓)3
=(∛240× ∛241× ∛242)/243
=(6.214 × 6.223 × 6.231)/ 243
Answer: (6.214 × 6.223 × 6.231)/ 243
Explanation
We used the fact that ((243)⅓)3=243 and then found the cube roots of 240,241, and 242 and simplified.
Problem 2
The length, breadth, and height of a cuboid is 5 unit, 4 unit, and 4.5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 243 cubic units.
Volume of a cuboid = length × breadth × height = 5 × 4 × 4.5 cubic units = 90 cubic units.
Given, Volume of a cube = 243 cubic units
⇒ side × side × side = 243 cubic units
⇒ side = ∛243
⇒ side = 6.24 units
Answer: Volume of the cuboid = 90 cubic units
Side length of the cube = 6.24 units
Explanation
Applied the formula and concept of the volume of a cuboid and cube and solved.
Problem 3
Multiply ∛243 × ∛216
∛243×∛216
= 6.24×6
= 37.44
Answer: 37.44
Explanation
We know that the cubic root of 216 is 6, hence multiplying ∛216 with ∛243.
Problem 4
What is ∛(243⁶^1/6) ?
∛(2436×1/6)
= (243)1/3
= 6.24…
Answer: 6.24
Explanation
We solved and simplified the exponent part first using the fact that, (2436×1/6)=243, then solved.
Problem 5
Find ∛(243-(-100)).
∛(243-(-100))
= ∛(243+100)
=∛343
=7
Answer: 7
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 243 Cube Root
1.What are perfect cube factors are included in 243?
2.Is 243 a perfect square?
3.What are the factors of 243?
4.Which power of 3 is 243?
5.What is 243 divisible by?
Important Glossaries for Cube Root of 243
- 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.
