Cube Root of 49

The cube root of 49 is 3.65930571002. The cube root of 49 is expressed as ∛49 in radical form, where the “ ∛ ”  sign" is called the “radical” sign. In exponential form, it is written as (49)^⅓. If “m” is the cube root of 49, then, m³=49. Let us find the value of “m”.

We can find cube root of 49 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 49.

Step 1: Let a=49. Let us take x as 3, since, 33=27 is the nearest perfect cube which is less than 49.

Step 2: Apply the formula.  ∛49≅ 3((3³+2×49) / (2(3)³+49))= 3.64…

Hence, 3.64… is the approximate cubic root of 49.
 

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

• 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.