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118 LearnersLast updated on October 1st, 2024
Cube Root of 4
The cube root of 4 is the value that, when multiplied by itself three times (cubed), gives the original number 4. 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 4?
The cube root of 4 is 1.58740105197. The cube root of 4 is expressed as ∛4 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (4)⅓. If “m” is the cube root of 4, then, m3=4. Let us find the value of “m”.
Finding the Cube Root of 4
The cube root of 4 is expressed as ∛4 as its simplest radical form,
since 4 = 2×2
∛4 = ∛(2×2)
Group together three same factors at a time and put the remaining factor under the ∛ .
∛4= ∛4
We can find cube root of 4 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 4 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 4.
Step 1: Let a=4. Let us take x as 1, since, 13=1 is the nearest perfect cube which is less than 4.
Step 2: Apply the formula. ∛4≅ 1((13+2×4) / (2(1)3+4))= 1.5
Hence, 1.5 is the approximate cubic root of 4.
Important Glossaries for Cube Root of 4
- Integers: Integers are numbers that can be positive, negative, or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. The examples of integers are, 1, 2, 5,8, -9, -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, which, on multiplication by itself, gives 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.