124 LearnersLast updated on May 26th, 2025
Cube Root of 27000
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 27000 and explain the methods used.
What is the Cube Root of 27000?
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, ∛27000 is written as 27000(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 27000, then y3 can be 27000. The cube root of 27000 is an exact value which is 30.
Finding the Cube Root of 27000
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 27000. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Estimation method
- Subtraction method
- Halley’s method
To find the cube root of a perfect cube number, the prime factorization method is often used. Since 27000 is a perfect cube, we can use this method.
Cube Root of 27000 by Prime Factorization Method
Let's find the cube root of 27000 using the prime factorization method.
Step 1: Find the prime factors of 27000.
27000 = 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5 × 5
Step 2: Group the prime factors in triples.
(2 × 2) × (3 × 3 × 3) × (5 × 5 × 5)
Step 3: Take one factor from each group.
The cube root of 27000 is 3 × 5 × 2 = 30.
The cube root of 27000 is 30.
Common Mistakes and How to Avoid Them in the Cube Root of 27000
Finding the perfect cube of a number without any errors can be a difficult task for the 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 non-perfect cube numbers.
Children sometimes assume that all numbers have whole-number cube roots.
For example: They might mistakenly think that a number like 27000, which is a perfect cube, cannot have a simple cube root because they don't know the factorization. To avoid this error, memorize the perfect cubes such as 27000, which is 30.
Cube Root of 27000 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 27000 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛27000 = 30 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 30 units.
Problem 2
A company manufactures 27000 cubic meters of material. Calculate the amount of material left after using 7000 cubic meters.
The amount of material left is 20000 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
27000 - 7000 = 20000 cubic meters.
Problem 3
A bottle holds 27000 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 35000 cubic meters.
Explanation
Let’s add the volume of both bottles:
27000 + 8000 = 35000 cubic meters.
Problem 4
When the cube root of 27000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 30 = 60
The cube of 60 = 216000
Explanation
When we multiply the cube root of 27000 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(23000 + 4000).
∛(23000 + 4000) = ∛27000 = 30
Explanation
As shown in the question ∛(23000 + 4000), we can simplify that by adding them.
So, 23000 + 4000 = 27000. Then we use this step: ∛27000 = 30 to get the answer.
FAQs on 27000 Cube Root
1.Can we find the Cube Root of 27000?
2.Why is the Cube Root of 27000 considered rational?
3.Is it possible to get the cube root of 27000 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 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 27000?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube Root of 27000?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube Root of 27000
- 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 which is expressed as (∛).
- Prime Factorization: The method of expressing a number as the product of its prime numbers.
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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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