119 LearnersLast updated on May 26th, 2025
Cube Root of -1728
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 -1728 and explain the methods used.
What is the Cube Root of -1728?
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, ∛-1728 is written as -1728^(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 -1728, then y^3 can be -1728. Since -1728 is a perfect cube, the cube root of -1728 is exactly -12.
Finding the Cube Root of -1728
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 -1728. The common methods we follow to find the cube root are given below: Prime factorization method Approximation method Subtraction method Halley’s method To find the cube root of a perfect number, we can use the prime factorization method. Since -1728 is a perfect cube, this method is suitable for finding its cube root.
Cube Root of -1728 by Prime Factorization
Let's find the cube root of -1728 using the prime factorization method. First, we find the prime factors of 1728: 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 Group the factors into triples: (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) Now, take one factor from each group: 2 × 2 × 3 = 12 Since the original number was negative, the cube root is also negative: ∛-1728 = -12 The cube root of -1728 is -12.
Common Mistakes and How to Avoid Them in the Cube Root of -1728
Finding the 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 cube roots for negative numbers as if they were positive.
Children sometimes try to calculate the cube root of negative numbers as if they were positive. For example: They might think that ∛-1728 should be 12 instead of -12. To avoid this error, remember that the cube root of a negative number is negative.
Mistake 2
Ignoring the exponent form
Most of us might forget that the cube root can also be written in exponent form. For example: Forgetting that the cube root of -1728 is -1728^(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 square root
Students may mistakenly calculate the square root instead of the cube root. For example, assuming the cube root of -1728 is √-1728. Remember that the cube root is a different operation than the square root.
Mistake 4
Using approximation methods for perfect cubes
Instead of using prime factorization for perfect cubes, students might use approximation methods unnecessarily. For example, trying to approximate the cube root of -1728 when it can be found exactly. Remember, for perfect cubes, use methods like prime factorization for exact results.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps. Ensure the whole calculation is done, then round the final result if necessary. However, for perfect cubes like -1728, rounding is unnecessary as the result is exact.
Cube Root of -1728 Examples:
Problem 1
Imagine you have a cube with a total volume of -1728 cubic units. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛-1728 = -12 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 -12 units.
Problem 2
A company processes -1728 cubic units of material. Calculate the amount of material left if 432 cubic units are removed.
The amount of material left is -2160 cubic units.
Explanation
To find the remaining material, we need to subtract the removed material from the total amount: -1728 - 432 = -2160 cubic units.
Problem 3
A container holds -1728 cubic units of liquid. Another container holds a volume of 256 cubic units. What would be the total volume if the containers are combined?
The total volume of the combined containers is -1472 cubic units.
Explanation
Explanation: Let's add the volume of both containers: -1728 + 256 = -1472 cubic units.
Problem 4
When the cube root of -1728 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-12) = -24 The cube of -24 = -13824
Explanation
When we multiply the cube root of -1728 by 2, it results in a significant change in volume because the cube increases exponentially.
Problem 5
Find ∛(-1296 - 432).
∛(-1296 - 432) = ∛-1728 = -12
Explanation
As shown in the question ∛(-1296 - 432), we simplify by subtracting them: -1296 - 432 = -1728. Then we use this step: ∛-1728 = -12 to get the answer.
FAQs on Cube Root of -1728
1.Can we find the Cube Root of -1728?
2.Why is Cube Root of -1728 rational?
3.Is it possible to get the cube root of -1728 as an exact number?
4.Can we find the cube root of a negative 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 -1728?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube Root of -1728?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube Root of -1728
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, -12 × -12 × -12 = -1728, therefore, -1728 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), ⅓ is the exponent which denotes the cube root of a. Radical sign: The symbol that is used to represent a root which is expressed as (∛). Rational number: A number that can be expressed as the quotient or fraction of two integers. The cube root of -1728 is rational because it is -12.
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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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