103 LearnersLast updated on May 26th, 2025
Cube Root of -64
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 -64 and explain the methods used.
What is the Cube Root of -64?
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, ∛-64 is written as (-64)^(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 -64, then y^3 can be -64. Since the cube root of -64 is an exact value, we can write it as -4.
Finding the Cube Root of -64
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 -64. The common methods we follow to find the cube root are given below: Prime factorization method Direct computation Approximation method To find the cube root of a perfect cube, like -64, the direct computation method is effective. Since -64 is a perfect cube, we can compute it directly as -4.
Cube Root of -64 by Direct Computation
Let's find the cube root of -64 using the direct computation method. Recognize that -64 is a perfect cube: -64 = (-4) × (-4) × (-4) Therefore, the cube root of -64 is -4.
Common Mistakes and How to Avoid Them in the Cube Root of -64
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 exact cube roots for non-perfect cube numbers.
Children might try to calculate an exact whole number for the cube root of numbers that are not perfect cubes. However, since -64 is a perfect cube, its cube root is an exact whole number: -4. To avoid errors, identify whether the number is a perfect cube first.
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 -64 is (-64)^(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
Assuming the cube root of a number is to divide it by 3 is incorrect. For example, mistakenly assuming ∛-64 is -64/3. To avoid this, remember that the cube root is the number that, when multiplied by itself three times, equals the original number.
Mistake 4
Using the wrong method for perfect cubes
Students might use complex methods like approximation for perfect cubes unnecessarily. For example, trying to approximate when they can directly compute for -64. Recognize perfect cubes and use direct computation to avoid unnecessary complexity.
Mistake 5
Overlooking negative signs in cube roots
Forgetting that the cube root of a negative number is also negative can lead to errors. For example, assuming ∛-64 is positive. To avoid this, remember that a negative number's cube root is negative because the product of three negative factors is negative.
Cube Root of -64 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of -64 cubic centimeters. Find the length of one side of the cube, equal to its cube root.
Side of the cube = ∛-64 = -4 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 -4 units.
Problem 2
A company produces -64 cubic meters of material in a theoretical experiment. Calculate the amount of material if the cube root is taken.
The cube root of the material is -4 cubic meters.
Explanation
To obtain the cube root of the volume, recognize that the negative sign remains, and the cube root of -64 is -4.
Problem 3
A container has a volume of -64 cubic meters. If another container has a volume of 16 cubic meters, what would be the total volume if the containers are combined?
The total volume of the combined containers is -48 cubic meters.
Explanation
Explanation: Let’s add the volume of both containers: -64 + 16 = -48 cubic meters.
Problem 4
When the cube root of -64 is multiplied by 2, calculate the resultant value.
2 × (-4) = -8
Explanation
When we multiply the cube root of -64 by 2, it results in -8, doubling the cube root value.
Problem 5
Find ∛(-32 - 32).
∛(-32 - 32) = ∛-64 = -4
Explanation
As shown in the question ∛(-32 - 32), we can simplify that by adding them. So, -32 - 32 = -64. Then we use this step: ∛-64 = -4 to get the answer.
FAQs on -64 Cube Root
1.Can we find the Cube Root of -64?
2.Why is Cube Root of -64 rational?
3.Is it possible to get the cube root of -64 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 Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Cube Root of -64?
8.How do technology and digital tools in Qatar support learning Algebra and Cube Root of -64?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Cube Root of -64
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, (-4) × (-4) × (-4) = -64, therefore, -64 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-64)^(1/3), ⅓ is the exponent which denotes the cube root of -64. Rational number: A number that can be expressed as a ratio of two integers. The cube root of -64 is rational because it is -4. Radical sign: The symbol that is used to represent a root, which is expressed as (∛).
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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.
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