117 LearnersLast updated on May 26th, 2025
Cube Root of 19683
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 19683 and explain the methods used.
What is the Cube Root of 19683?
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, ∛19683 is written as 19683(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 19683, then y³ can be 19683. Since 19683 is a perfect cube, its cube root is exactly 27.
Finding the Cube Root of 19683
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 19683. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
For 19683, which is a perfect cube, one of the simplest methods is the prime factorization method.
Cube Root of 19683 by Prime Factorization Method
Let's find the cube root of 19683 using the prime factorization method. First, find the prime factors of 19683:
19683 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 39
To find the cube root, group the factors into triples: (3 × 3 × 3) × (3 × 3 × 3) × (3 × 3 × 3)
Each group gives a factor of 3, and there are three groups.
Thus, the cube root of 19683 is 3 × 3 × 3 = 27.
Common Mistakes and How to Avoid Them in the Cube Root of 19683
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 the students commonly make and the ways to avoid them:
Mistake 1
Trying to find cube roots without considering prime factorization.
Students might overlook prime factorization, assuming they need to use complex methods.
For example, they might try approximation unnecessarily. Remember that prime factorization is effective for perfect cubes like 19683.
Cube Root of 19683 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 19683 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛19683 = 27 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 27 units.
Problem 2
A company manufactures 19683 cubic meters of material. Calculate the amount of material left after using 5000 cubic meters.
The amount of material left is 14683 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
19683 - 5000 = 14683 cubic meters.
Problem 3
A bottle holds 19683 cubic meters of volume. Another bottle holds a volume of 2000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 21683 cubic meters.
Explanation
Let’s add the volume of both bottles:
19683 + 2000 = 21683 cubic meters.
Problem 4
When the cube root of 19683 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 27 = 54 The cube of 54 = 157464
Explanation
When we multiply the cube root of 19683 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(5000 + 14683).
∛(5000 + 14683) = ∛19683 = 27
Explanation
As shown in the question ∛(5000 + 14683), we can simplify that by adding them.
So, 5000 + 14683 = 19683.
Then we use this step: ∛19683 = 27 to get the answer.
FAQs on 19683 Cube Root
1.Can we find the Cube Root of 19683?
2.Why is the Cube Root of 19683 rational?
3.Is it possible to get the cube root of 19683 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 19683
- 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, 3 × 3 × 3 = 27, therefore, 27 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 is expressed as (∛).
- Rational number: A number that can be expressed as a fraction or whole number. The cube root of 19683 is rational because it is 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.
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: He loves to play the quiz with kids through algebra to make kids love it.
