Cube Root of 40

The cube root of 40 is the value which, when multiplied by itself three times (cubed), gives the original number 40. The cube root of 40 is 3.41995189335.  The cube root of 40 is expressed as ∛40 in radical form, where the “ ∛ ”  sign” is called the “radical” sign. In exponential form, it is written as (40)^⅓. If “m” is the cube root of 40, then, m³=40. Let us find the value of “m”.
 

We can find cube root of 40 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 48.

Step 1: Let a=40. Let us take x as 3, since, 3³=27 is the nearest perfect cube which is less than 40.

Step 2: Apply the formula.  ∛40≅ 3((3³+2×40) / (2(3)³+40))= 3.41…

Hence, 3.41… is the approximate cubic root of 40.
 

• Cube root properties - The features when cube root is applied to any number. Those are:

 

1) The cube root of all odd numbers is an odd number. The same applies for even numbers also, that is, the cube of any even number is even. 

2) The cube root of a negative number is also negative.

3) If the cube root of a number is a whole number, then that original number is said to be perfect cube

 

• Irrational Numbers - Numbers which cannot be expressed as m/n form, where m and n are integers and n not equal to 0, are called Irrational numbers.

 

• Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be found out.

 

• 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 near to the correct answer, but not perfectly correct.

 

• Iterative method - This method is a mathematical process which uses an initial value to generate a further sequence of solutions for a problem, step-by-step.