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169 LearnersLast updated on November 30th, 2024
Cube Root of 25
The cube root of 25 is the value which, when multiplied by itself three times (cubed), gives the original number 25. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, creating unique digital art etc.
What Is the Cube Root of 25?
The cube root of 25 is 2.92401773821. The cube root of 25 is expressed as ∛25 in radical form, where the “ ∛ “ sign is called the “radical” sign. In exponential form, it is written as (25)1/3. If “m” is the cube root of 25, then, m3=25. Let us find the value of “m”.
Finding the Cube Root of 25
The Prime Factorization of 25 is 5×5, so, the cube root of 25 is expressed as ∛25 as its simplest radical form. We can find the cube root of 25 through a method, named Halley’s Method. Let us see how it finds the result.
Cube Root of 25 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 25.
Step 1: Let a=25. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 25.
Step 2: Apply the formula. ∛25≅ 2((23+2×25) / (2(2)3+25))= 2.82…
Hence, 2.82… is the approximate cubic root of 25.
Important Glossaries for Cube Root of 25
- 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. These cannot be in fractional or decimal form.
- Square root -The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.
- 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, as if the approximate value is just near and close the original value.
- Iterative method - This method is a process, used in mathematics, which uses an initial value to generate further and step-by-step sequence of solutions for a problem.