131 LearnersLast updated on May 26th, 2025
Cube Root of 125/216
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 125/216 and explain the methods used.
What is the Cube Root of 125/216?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.
In exponential form, ∛(125/216) is written as (125/216)(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 125/216, then y3 can be 125/216. Since 125 and 216 are both perfect cubes, we can express the cube root of 125/216 as (∛125)/(∛216), which simplifies to 5/6.
Finding the Cube Root of 125/216
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 125/216. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Simplification method
Since 125/216 is a fraction made of perfect cubes, we can use the simplification method to find its cube root.
Cube Root of 125/216 by Simplification Method
Let's find the cube root of 125/216 using the simplification method.
The formula is ∛(a/b) = (∛a)/(∛b) where: a = the numerator b = the denominator
Substituting, a = 125; b = 216 ∛(125/216)
= (∛125)/(∛216)
Since 125 = 53 and 216 = 63, we find:
∛125 = 5 and ∛216 = 6
Thus, ∛(125/216) = 5/6
The cube root of 125/216 is 5/6.
Common Mistakes and How to Avoid Them in Finding the Cube Root of 125/216
Finding the cube root of a fraction without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Students sometimes mistakenly try to find an exact whole number for cube roots of fractions like 125/216, which are actually composed of perfect cubes. For example, they may assume a more complex process is needed. To avoid this error, recognize that simplifying perfect cubes is straightforward.
Cube Root of 125/216 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 125/216 cubic meters. Find the length of one side of the toy equal to its cube root.
Side of the cube = ∛(125/216) = 5/6 meters
Explanation
To find the side of the cube, we need to find the cube root of the given volume.
Therefore, the side length of the cube is 5/6 meters.
Problem 2
A company manufactures material in a volume of 125 cubic meters. After using 27 cubic meters, find the cube root of the remaining volume.
The cube root of the remaining volume is ∛98.
Explanation
To find the remaining material, subtract the used material from the total amount:
125 - 27 = 98 cubic meters.
The cube root of 98 is approximately 4.62.
Problem 3
A bottle holds 125 cubic meters of volume. Another bottle holds a volume of 216 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 341 cubic meters.
Explanation
Let’s add the volume of both bottles:
125 + 216 = 341 cubic meters.
Problem 4
When the cube root of 125/216 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (5/6) = 5/3
The cube of 5/3 = 125/27
Explanation
When we multiply the cube root of 125/216 by 2, it results in an increase in the cube because the cube of the new value, 5/3, is 125/27.
Problem 5
Find ∛(250/432).
∛(250/432) ≈ 0.83
Explanation
The cube root of 250/432 is approximately 0.83, as neither 250 nor 432 is a perfect cube.
FAQs on Cube Root of 125/216
1.Can we find the Cube Root of 125/216 exactly?
2.Why is Cube Root of 125/216 rational?
3.Is it possible to get the cube root of 125/216 as a whole number?
4.Can we find the cube root of any fraction using the simplification method?
5.Is there any formula to find the cube root of a fraction?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube Root of 125/216?
8.How do technology and digital tools in Singapore support learning Algebra and Cube Root of 125/216?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Cube Root of 125/216
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself, resulting in a whole number. For example, 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In the context of cube roots, ⅓ is the exponent indicating the cube root of a number.
- Radical sign: The symbol used to represent a root, expressed as (∛).
- Rational number: The numbers that can be expressed as the quotient of two integers are rational. For example, the cube root of 125/216 is rational because it simplifies to 5/6.
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About BrightChamps in Singapore
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.
