428 LearnersLast updated on May 26th, 2025
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 β25 in radical form, where the “ β “ 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 β25 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 Halleyβs 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 βa≅ 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. β25≅ 2((23+2×25) / (2(2)3+25))= 2.82…
Hence, 2.82… is the approximate cubic root of 25.
Common Mistakes and How to Avoid Them in the Cube Root of 25
some common mistakes with their solutions are given below:
Mistake 1
Children get confused of the concept of cube root with that of square root.
The Cube root of 25 is β25, and the square root of 25 is √25. Understand the definition of Cube roots and square root.
Mistake 2
Misidentifying prime numbers with composite numbers while doing prime factorization to find cube roots.
While prime factorization, make sure you know which numbers are prime and which are not. Have a clear vision on prime numbers and composite numbers before applying the Prime Factorization method.
Mistake 3
Applying exponent rules incorrectly when finding cube roots.
β25 is not same as 253. β25 =2.92… and 253=15625.
Mistake 4
Students often calculate mentally the value of cube roots.
Students can use Prime factorization method or Halley’s method to find out the approximate value for cube roots.
Mistake 5
Not checking for perfect cubes, like that of 8, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 100.
Cube Root of 25 Examples
Problem 1
Find β25/ β14
β25/ β14
= 2.924 / 2.410
= 2924/2410
=1.213
Answer: 1.213
Explanation
We found that the cubic root of 14 is 2.410…, hence dividing β25 by β14.
Problem 2
The Volume of a cube is 25 cubic centimeters, find the length of one side of the cube.
We know that, (side of a cube)3 = Volume of a cube
⇒side of the cube = β(Volume of the cube)
⇒side of the cube = β25
⇒ side of the cube = 2.924 cm
Answer: 2.924 cm
Explanation
We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
Problem 3
Subtract β25 - β8, β27-β25
β25-β8
= 2.924–2
=0.924
β27-β25
= 3-2.924
= 0.076
Answer: 0.924, 0.076
Explanation
We know that the cubic root of 8 is 2, hence subtracting β8 from β25. Applying the same for the next one, we know that the cubic root of 27 is 3, hence subtracting β25 from β27.
Problem 4
What is β(25Β²) ?
β(252)
= β625
= 8.549…
Answer: 8.549…
Explanation
We first found the square value of 25, which is 625, and then found out the cube root of 625.
Problem 5
Find β((25+2)Γ(25+39)).
β((25+2)×(25+39))
= β(27×64)
=β1728
= 12
Answer: 12
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 25 Cube Root
1.What does 3β27 mean ?
2.Is 25 a perfect cube?
3.What is 25 cubes?
4.How to find cube roots?
5.Is 45 a perfect cube?
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.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
