Cube Root of 7

The cube root of 7 is 1.91293118277. The cube root of 7 is expressed as ∛7 in radical form, where the “∛"  sign is called the “radical” sign. In exponential form, it is written as (7)^⅓. If “m” is the cube root of 7, then, m³=7.  Let us find the value of “m”.
 

The Prime Factorization of 7 is 7, so, the cube root of 7 is expressed as ∛7 as its simplest radical form. We can find cube root of 7 through another 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 7.

Step 1: Let a=7. Let us take x as 1, since, 1 is the nearest perfect cube which is less than 7.

Step 2: Apply the formula.  ∛7≅ 1((1³+2×7) / (2(1)³+7))=15/9 ≅ 1.667

Hence, 1.667 is the approximate cubic root of 7.
 

• 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.

• 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.