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Last updated on ** October 1st, 2024**

The cube root of 7 is the value that, when multiplied by itself three times (cubed), gives the original number 7. Do you know? Cube roots apply to our real life also, like that for measuring volume and scaling, density and mass calculation, etc.

The cube root of 7 is 1.91293118277. The cube root of 7 is expressed as β7 in radical form, where the “β" sign is called the “radical” sign. In exponential form, it is written as (7)^{β
}. If “m” is the cube root of 7, then, m^{3}=7. Let us find the value of “m”.

The Prime Factorization of 7 is 7, so, the cube root of 7 is expressed as β7 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 βa≅ x((x^{3}+2a) / (2x^{3}+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. β7≅ 1((1^{3}+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.