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133 LearnersLast updated on November 30th, 2024
Cube Root of 243
The cube root of 243 is the value that, when multiplied by itself three times (cubed), gives the original number 243. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, field of engineering etc.
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.
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.