110 LearnersLast updated on May 26th, 2025
Cube Root of 2197
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 2197 and explain the methods used.
What is the Cube Root of 2197?
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, ∛2197 is written as 2197(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 2197, then y3 can be 2197. Since 2197 is a perfect cube, we find that the cube root of 2197 is exactly 13.
Finding the Cube Root of 2197
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 2197. 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 cube number, we often follow the prime factorization method.
Since 2197 is a perfect cube, we use the prime factorization method.
Cube Root of 2197 by Prime Factorization Method
Let's find the cube root of 2197 using the prime factorization method. The steps are:
Step 1: Find the prime factors of 2197.
Step 2: Group the factors in triples.
Step 3: The cube root is the product of one factor from each group. Prime factorization of 2197 gives us 13 × 13 × 13.
The cube root of 2197 is 13.
Common Mistakes and How to Avoid Them in the Cube Root of 2197
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 approximate cube roots for perfect cube numbers.
Students sometimes try to approximate the cube root of numbers like 2197, which are perfect cubes.
For example: They might assume they need to round the result. To avoid this error, recognize that some numbers have a perfect cube root, that is, the cube root of 2197 is exactly 13.
Cube Root of 2197 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 2197 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛2197 = 13 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 13 units.
Problem 2
A company manufactures 2197 cubic meters of material. Calculate the amount of material left after using 2000 cubic meters.
The amount of material left is 197 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
2197 - 2000 = -3 cubic meters. (Note: This was a mistake in the original question; the calculation should ensure the used amount is less than the total).
Problem 3
A bottle holds 2197 cubic meters of volume. Another bottle holds a volume of 300 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 2497 cubic meters.
Explanation
Let’s add the volume of both bottles:
2197 + 300 = 2497 cubic meters.
Problem 4
When the cube root of 2197 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 13 = 26 The cube of 26 = 17576
Explanation
When we multiply the cube root of 2197 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(1000+1197).
∛(1000+1197) = ∛2197 = 13
Explanation
As shown in the question ∛(1000+1197), we can simplify that by adding them.
So, 1000 + 1197 = 2197.
Then we use this step: ∛2197 = 13 to get the answer.
FAQs on 2197 Cube Root
1.Can we find the Cube Root of 2197?
2.Why is Cube Root of 2197 rational?
3.Is it possible to get the cube root of 2197 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 United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube Root of 2197?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 2197?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 2197
- 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: 13 × 13 × 13 = 2197, therefore, 2197 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 2197(1/3), ⅓ is the exponent which denotes the cube root of 2197.
- 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 a whole number. The cube root of 2197 is rational because it is a whole number (13).
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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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