122 LearnersLast updated on May 26th, 2025
Cube Root of 1331000
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 1331000 and explain the methods used.
What is the Cube Root of 1331000?
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, ∛1331000 is written as 1331000(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 1331000, then y³ can be 1331000. The cube root of 1331000 is an exact value, which is 110.
Finding the Cube Root of 1331000
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 1331000. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Estimation method
- Halley’s method
To find the cube root of a perfect cube number, we can follow the prime factorization method. Since 1331000 is a perfect cube, prime factorization is an efficient method here.
Cube Root of 1331000 by Prime Factorization
Let's find the cube root of 1331000 using the prime factorization method.
First, we perform prime factorization of 1331000: 1331000 = 2 × 2 × 2 × 5 × 5 × 5 × 11 × 11 × 11
Grouping the prime factors in triples: (2 × 2 × 2) × (5 × 5 × 5) × (11 × 11 × 11)
Taking the cube root of each group gives us: ∛1331000 = 2 × 5 × 11 = 110
Therefore, the cube root of 1331000 is 110.
Common Mistakes and How to Avoid Them in Finding the Cube Root of 1331000
Finding the perfect cube of a number without any errors can be a challenging 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
Assuming non-perfect cubes for perfect cube numbers.
Students may mistakenly assume that numbers like 1331000 are not perfect cubes and try to approximate.
For example, they might believe there's no exact whole number cube root for 1331000. To avoid this, remember that 1331000 is a perfect cube, and its cube root is exactly 110.
Cube Root of 1331000 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 1331000 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛1331000 = 110 cm
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 110 cm.
Problem 2
A company manufactures 1331000 cubic meters of material. Calculate the amount of material left after using 100000 cubic meters.
The amount of material left is 1231000 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 1331000 - 100000 = 1231000 cubic meters.
Problem 3
A container holds 1331000 cubic meters of volume. Another container holds a volume of 1000 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 1332000 cubic meters.
Explanation
Explanation: Let’s add the volume of both containers: 1331000 + 1000 = 1332000 cubic meters.
Problem 4
When the cube root of 1331000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 110 = 220 The cube of 220 = 10648000
Explanation
When we multiply the cube root of 1331000 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(1000000+331000).
∛(1000000+331000) = ∛1331000 = 110
Explanation
As shown in the question ∛(1000000+331000), we can simplify that by adding them. So, 1000000 + 331000 = 1331000. Then we take the cube root to get the answer, which is 110.
FAQs on Cube Root of 1331000
1.Can we find the Cube Root of 1331000?
2.Why is the Cube Root of 1331000 a rational number?
3.Is it possible to get the cube root of 1331000 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 1331000?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube Root of 1331000?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube Root of 1331000
- 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, 110 × 110 × 110 = 1331000, therefore, 1331000 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 (∛).
- Rational number: A number that can be expressed as a fraction or an exact value. For example, the cube root of 1331000 is rational because it is exactly 110.
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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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