102 LearnersLast updated on May 26th, 2025
Cube Root of -2
A number that 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 -2 and explain the methods used.
What is the Cube Root of -2?
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, ∛-2 is written as (-2)^(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 -2, then y^3 can be -2. Since the cube root of -2 is not an exact whole number, we can write it as approximately -1.2599.
Finding the Cube Root of -2
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 -2. The common methods we follow to find the cube root are given below:
- Approximation method
- Newton's method
To find the cube root of a non-perfect cube, we often follow approximation or Newton's method.
Since -2 is not a perfect cube, we use these methods.
Cube Root of -2 by Newton's Method
Let's find the cube root of -2 using Newton's method.
The formula is: x_(n+1) = x_n - (x_n^3 + a) / (3 * x_n^2)
where: a = the number for which the cube root is being calculated
x_n = initial approximation Substituting,
a = -2; x_0 = -1
x_1 = -1 - ((-1)^3 + (-2)) / (3 * (-1)^2)
x_1 = -1 - (-1 + 2) / 3 x_1 = -1 - 1/3
x_1 ≈ -1.3333
Refining the approximation further gives us approximately -1.2599.
Common Mistakes and How to Avoid Them in the Cube Root of -2
Finding the cube root of a number without any errors can be a challenging 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 perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers like -2, which are not perfect cubes.
For example: They assume they would get an exact whole number for -2 like they do for 8 (since 2^3 = 8). To avoid this error, remember that some numbers don't have a perfect cube root, such as the cube root of -2, which is approximately -1.26.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that cube root can also be written in exponent form.
For example: Forgetting that the cube root of -2 can be written as (-2)^(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 -2 is the number they multiply by itself three times to get -2, not dividing -2 by 3.
Mistake 4
Using inappropriate methods for non-perfect cubes
Instead of using suitable methods like approximation or Newton's method for non-perfect cubes, children might attempt to use prime factorization. Remember that prime factorization is not effective for non-perfect cubes like -2. Use the approximation method or Newton's method instead.
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 -2 to -1.3 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result.
Cube Root of -2 Examples:
Problem 1
Imagine you have a cube-shaped object that has a total volume of -2 cubic centimeters. What would be the length of one side of the cube?
Side of the cube = ∛-2 = -1.26 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 -1.26 units.
Problem 2
A company has a chemical solution with a concentration of -2 grams per cubic meter. If they remove 1 gram per cubic meter, what will be the new concentration?
The new concentration is -3 grams per cubic meter.
Explanation
To find the new concentration, we need to subtract the removed concentration from the original value: -2 - 1 = -3 grams per cubic meter.
Problem 3
In a hypothetical scenario, a container holds -2 cubic meters of a material. If another container holds 1 cubic meter, what would be the total volume if the materials were combined?
The total volume of the combined materials is -1 cubic meter.
Explanation
To find the total volume, add the volumes of both containers: -2 + 1 = -1 cubic meter.
Problem 4
When the cube root of -2 is multiplied by 3, calculate the resultant value.
3 × -1.26 = -3.78
Explanation
Multiplying the cube root of -2 by 3 results in a linear increase in this value.
Problem 5
Find ∛(-3 + 1).
∛(-3 + 1) = ∛-2 ≈ -1.26
Explanation
As shown in the question ∛(-3 + 1), we can simplify that by adding them.
So, -3 + 1 = -2.
Then we use this step: ∛-2 ≈ -1.26 to get the answer.
FAQs on -2 Cube Root
1.Can we find the Cube Root of -2?
2.Why is the Cube Root of -2 irrational?
3.Is it possible to get the cube root of -2 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 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 -2?
8.How do technology and digital tools in Singapore support learning Algebra and Cube Root of -2?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Cube Root of -2
- 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. For example, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-2)^(1/3), ⅓ is the exponent which denotes the cube root of -2.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of -2 is irrational because its decimal form goes on continuously without repeating.
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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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