102 LearnersLast updated on May 26th, 2025
Cube Root of -3
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 understanding the properties of materials and designing structures. We will now find the cube root of -3 and explain the methods used.
What is the Cube Root of -3?
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, ∛-3 is written as (-3)^(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 -3, then y^3 can be -3. Since the cube root of -3 is not an exact value, we can write it as approximately -1.4422.
Finding the Cube Root of -3
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 -3. The common methods we follow to find the cube root are given below:
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a non-perfect number, we often follow Halley’s method.
Since -3 is not a perfect cube, we use Halley’s method.
Cube Root of -3 by Halley’s method
Let's find the cube root of -3 using Halley’s method.
The formula is ∛a ≅ x((x^3 + 2a) / (2x^3 + a))
where:
a = the number for which the cube root is being calculated
x = the nearest perfect cube Substituting,
a = -3; x = -1
∛a ≅ -1(((-1)^3 + 2 × (-3)) / (2 × (-1)^3 + (-3)))
∛-3 ≅ -1((-1 - 6) / (-2 - 3)) ∛-3 ≅ -1.442
The cube root of -3 is approximately -1.4422.
Common Mistakes and How to Avoid Them in the Cube Root of -3
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes that students commonly make and the ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers like -3, which are not perfect cubes.
For example: They assume that they would get an exact whole number for -3 like they get for 8 (since ∛8 = 2).
To avoid this error, memorize that some numbers don't have a perfect cube root, that is, the cube root of -3 is approximately -1.4422.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that the cube root can also be written in exponent form.
For example: Forgetting that the cube root of -3 is (-3)^(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
To avoid this, children should remember that the cube root of -3 is the number they multiply by itself three times to get -3.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, children end up using prime factorization. For example, they might try to find the cube root of -3 by breaking it down into its prime factors. Remember that prime factorization can help analyze a number's factors, but it's not the best method for non-perfect cubes. Since -3 is a non-perfect cube, you can use either the approximation method or Halley’s method.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps. For example: we might round the cube root of -3 to -1.4 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result.
Cube Root of -3 Examples:
Problem 1
Imagine you have a cube-shaped object that has a total volume of -3 cubic units. Find the length of one side of the object equal to its cube root.
Side of the cube = ∛-3 ≈ -1.44 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 approximately -1.44 units.
Problem 2
A company has a material with a volume of -3 cubic meters. If the material is divided equally into 3 parts, what is the volume of each part?
The volume of each part is -1 cubic meters.
Explanation
To find the volume of each part, we need to divide the total volume by 3: -3 / 3 = -1 cubic meters.
Problem 3
A container holds -3 cubic liters of liquid. If another container holds 5 cubic liters, what would be the total volume if the containers are combined?
The total volume of the combined containers is 2 cubic liters.
Explanation
Explanation: Let’s add the volume of both containers: -3 + 5 = 2 cubic liters.
Problem 4
When the cube root of -3 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-1.44) = -2.88 The cube of -2.88 = -23.87
Explanation
When we multiply the cube root of -3 by 2, it results in a significant change in the volume because the cube increases exponentially.
Problem 5
Find ∛(-3 + 5).
∛(-3 + 5) = ∛2 ≈ 1.26
Explanation
As shown in the question ∛(-3 + 5), we can simplify that by adding them. So, -3 + 5 = 2. Then we use this step: ∛2 ≈ 1.26 to get the answer.
FAQs on Cube Root of -3
1.Can we find the Cube Root of -3?
2.Why is the Cube Root of -3 irrational?
3.Is it possible to get the cube root of -3 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 Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Cube Root of -3?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube Root of -3?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube Root of -3
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. A perfect cube always results in a whole number. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-3)^(1/3), ⅓ is the exponent which denotes the cube root of -3. Radical sign: The symbol used to represent a root, expressed as (∛). Irrational number: Numbers that cannot be put in fractional forms are irrational. For example, the cube root of -3 is irrational because its decimal form goes on continuously without repeating the numbers.
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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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