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”.
 

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.
 

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.
 

• 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.