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135 LearnersLast updated on November 30th, 2024
Cube Root of 75
The cube root of 75 is the value that, when multiplied by itself three times (cubed), gives the original number 75. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.
What Is the Cube Root of 75 ?
The cube root of 75 is 4.21716332651. The cube root of 75 is expressed as ∛75 in radical form, where the “∛" sign is called the “radical” sign. In exponential form, it is written as (75)⅓. If “m” is the cube root of 75, then, m3=75. Let us find the value of “m”.
Finding the Cube Root of 75
The cube root of 75 is expressed as ∛75 as its simplest radical form,
since 75 = 5×5×3
∛75 = ∛(5×5×3)
Group together three same factors at a time and put the remaining factor under the ∛ .
∛75= ∛75
We can find cube root of 75 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 75 By Halley’s Method
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 75.
Step 1: Let a=75. Let us take x as 4, since, 43=64 is the nearest perfect cube which is less than 75.
Step 2: Apply the formula. ∛75≅ 4((43+2×75) / (2(4)3+75))= 4.12…
Hence, 4.12… is the approximate cubic root of 75.
Important Glossaries for Cube Root of 75
- 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.
- 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.