123 LearnersLast updated on May 26th, 2025
Cube Root of 195112
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 195112 and explain the methods used.
What is the Cube Root of 195112?
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, ∛195112 is written as 195112(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 195112, then y3 can be 195112. Since 195112 is a perfect cube, its cube root is an exact value, which is 58.
Finding the Cube Root of 195112
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 195112. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 195112 is a perfect cube, the prime factorization method is efficient in this case.
Cube Root of 195112 by Prime Factorization
Let's find the cube root of 195112 using the prime factorization method.
First, find the prime factors of 195112:
195112 = 23 × 32 × 7 × 133.
To find the cube root, take the cube root of each factor: ∛(23 × 32 × 7 × 133) = 2 × 13 = 26.
Therefore, the cube root of 195112 is 58.
Common Mistakes and How to Avoid Them in the Cube Root of 195112
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 perfect cube roots for non-perfect cube numbers.
Children always try to calculate an exact whole number for the cube root of numbers like 195112, which are perfect cubes.
For example, they might mistakenly assume it isn't a perfect cube. To avoid this error, verify if the number is a perfect cube first, like 195112 is, which has a cube root of 58.
Cube Root of 195112 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 195112 cubic centimeters. Find the length of one side of the container equal to its cube root.
Side of the cube = ∛195112 = 58 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 58 units.
Problem 2
A company manufactures 195112 cubic meters of material. Calculate the amount of material left after using 112000 cubic meters.
The amount of material left is 83112 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
195112 - 112000 = 83112 cubic meters.
Problem 3
A bottle holds 195112 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 203112 cubic meters.
Explanation
Let’s add the volume of both bottles:
195112 + 8000 = 203112 cubic meters.
Problem 4
When the cube root of 195112 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 58 = 116 The cube of 116 = 1560896
Explanation
When we multiply the cube root of 195112 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(46000 + 149112).
∛(46000 + 149112) = ∛195112 = 58
Explanation
As shown in the question ∛(46000 + 149112), we can simplify that by adding them.
So, 46000 + 149112 = 195112.
Then we use this step: ∛195112 = 58 to get the answer.
FAQs on 195112 Cube Root
1.Can we find the Cube Root of 195112?
2.Why is Cube Root of 195112 rational?
3.Is it possible to get the cube root of 195112 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 Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube Root of 195112?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube Root of 195112?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube Root of 195112
- 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: 58 × 58 × 58 = 195112, therefore, 195112 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 195112(1/3), ⅓ is the exponent which denotes the cube root of 195112.
- 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 ratio of two integers. The cube root of 195112 is rational because it is a whole number.
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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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