104 LearnersLast updated on May 26th, 2025
Cube Root of -125
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 and explain the methods used.
What is the Cube Root of -125?
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 is written as (-125)^(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, then y^3 can be -125. The cube root of -125 is exactly -5, because (-5) × (-5) × (-5) = -125.
Finding the Cube Root of -125
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. The common methods we follow to find the cube root are given below: Prime factorization method Approximation method Subtraction method Halley’s method Since -125 is a perfect cube, we can use the prime factorization method to find the cube root.
Cube Root of -125 by Prime Factorization
Let's find the cube root of -125 using the prime factorization method. First, find the prime factors of -125: -125 = -1 × 5 × 5 × 5 To find the cube root, group the factors in triples: ∛(-1 × 5 × 5 × 5) = -5 Therefore, the cube root of -125 is -5, since (-5) × (-5) × (-5) = -125.
Common Mistakes and How to Avoid Them in the Cube Root of -125
Finding the perfect cube root of a number without any errors can be a difficult task for 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 non-negative cube roots for negative numbers
Children often mistakenly assume that the cube root of a negative number must be positive or not exist. For example: They might think the cube root of -125 should be positive. To avoid this error, remember that cube roots of negative numbers are also negative.
Mistake 2
Ignoring the exponent form
Most of us might forget that cube roots can also be written in exponent form. For example: Forgetting that the cube root of -125 is (-125)^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
Some students mistakenly assume the cube root of -125 is simply dividing -125 by 3. To avoid this, remember that the cube root of -125 is the number that, when multiplied by itself three times, results in -125.
Mistake 4
Using approximation methods for perfect cubes
Instead of using the prime factorization method for perfect cubes, students might use approximation methods unnecessarily. Remember that for perfect cubes like -125, the prime factorization method is straightforward and exact.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps. For example: they might prematurely round the cube root of a calculated approximation. To avoid this, ensure the whole calculation is done, then round the final result if needed. However, in the case of -125, no rounding is necessary as it is a perfect cube.
Cube Root of -125 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of -125 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛-125 = -5 units
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 exactly -5 units.
Problem 2
A company manufactures -125 cubic meters of a material. Calculate the amount of material left after using -50 cubic meters.
The amount of material left is -75 cubic meters.
Explanation
To find the remaining material, subtract the used material from the total amount: -125 - (-50) = -125 + 50 = -75 cubic meters.
Problem 3
A bottle holds -125 cubic meters of volume. Another bottle holds a volume of -8 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is -133 cubic meters.
Explanation
Explanation: Add the volume of both bottles: -125 + (-8) = -133 cubic meters.
Problem 4
When the cube root of -125 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-5) = -10 The cube of -10 = -1000
Explanation
When we multiply the cube root of -125 by 2, it results in a greater change in volume because the cube increases exponentially.
Problem 5
Find ∛(-64 + -61).
∛(-64 + -61) = ∛-125 = -5
Explanation
As shown in the question ∛(-64 + -61), we can simplify that by adding them. So, -64 + -61 = -125. Then we use this step: ∛-125 = -5 to get the answer.
FAQs on -125 Cube Root
1.Can we find the Cube Root of -125?
2.Why is the Cube Root of -125 not irrational?
3.Is it possible to get the cube root of -125 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube Root of -125?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube Root of -125?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube Root of -125
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 that is the product of multiplying a number three times by itself. 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 cube roots, ⅓ is the exponent which denotes the cube root of a number. Radical sign: The symbol that is used to represent a root, expressed as (∛). Negative number: A number that is less than zero, which can also have a real cube root as indicated in this example with -125.
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Jaskaran Singh Saluja
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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.
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