117 LearnersLast updated on May 26th, 2025
Cube Root of 32768
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 32768 and explain the methods used.
What is the Cube Root of 32768?
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, ∛32768 is written as 32768(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 32768, then y3 = 32768. Since the cube root of 32768 is an exact value, we can find it precisely as 32.
Finding the Cube Root of 32768
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 32768. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 32768 is a perfect cube, the prime factorization method is efficient for finding its cube root.
Cube Root of 32768 by Prime Factorization Method
Let's find the cube root of 32768 using the prime factorization method.
First, express 32768 as a product of its prime factors.
32768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 215
To find the cube root, group the prime factors in triples: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)
Each group of (2 × 2 × 2) is 8, and there are five such groups,
so: ∛(215) = 2(15/3) = 25 = 32
Therefore, the cube root of 32768 is 32.
Common Mistakes and How to Avoid Them in the Cube Root of 32768
Finding the perfect cube of a number without any errors can be a difficult task for students. Here are a few mistakes they commonly make and the ways to avoid them:
Mistake 1
Trying to find cube roots without recognizing perfect cubes.
Students sometimes assume numbers are not perfect cubes when they are.
For example, 32768 is a perfect cube, but some might not recognize it. To avoid this error, check whether a number can be broken into triplet factors.
Cube Root of 32768 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 32768 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛32768 = 32 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 32 units.
Problem 2
A company manufactures 32768 cubic meters of material. Calculate the amount of material left after using 12000 cubic meters.
The amount of material left is 20768 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
32768 - 12000 = 20768 cubic meters.
Problem 3
A bottle holds 32768 cubic meters of volume. Another bottle holds a volume of 8000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 40768 cubic meters.
Explanation
Let’s add the volume of both bottles:
32768 + 8000 = 40768 cubic meters.
Problem 4
When the cube root of 32768 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 32 = 64
The cube of 64 = 262144
Explanation
When we multiply the cube root of 32768 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(32000 + 768).
∛(32000 + 768) = ∛32768 = 32
Explanation
As shown in the question ∛(32000 + 768), we can simplify that by adding them.
So, 32000 + 768 = 32768.
Then we use this step: ∛32768 = 32 to get the answer.
FAQs on 32768 Cube Root
1.Can we find the Cube Root of 32768?
2.Why is the Cube Root of 32768 rational?
3.Is it possible to get the cube root of 32768 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?
Important Glossaries for Cube Root of 32768
- 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 32768(1/3), ⅓ is the exponent which denotes the cube root of 32768.
- Radical sign: The symbol that is used to represent a root which is expressed as (∛).
- Rational number: A number that can be expressed as a fraction or ratio of two integers. For example, the cube root of 32768 is rational because it is 32, a whole number.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
