105 LearnersLast updated on May 26th, 2025
Cube Root of 0.001728
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 0.001728 and explain the methods used.
What is the Cube Root of 0.001728?
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, ∛0.001728 is written as 0.001728^(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 0.001728, then y^3 can be 0.001728. Since the cube root of 0.001728 is an exact value, it is 0.12.
Finding the Cube Root of 0.001728
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 0.001728. 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 number, we often use the prime factorization method if the number is a perfect cube. Since 0.001728 is a perfect cube, we can use the prime factorization method.
Cube Root of 0.001728 by Prime Factorization Method
Let's find the cube root of 0.001728 using the prime factorization method. First, express the number as a fraction: 0.001728 = 1728/1000000. Now, find the prime factorization of the numerator and the denominator: 1728 = 2^6 × 3^3 1000000 = 10^6 = (2^6 × 5^6) Taking the cube root of both the numerator and the denominator: ∛(1728/1000000) = (∛1728)/(∛1000000) = (∛(2^6 × 3^3))/(∛(2^6 × 5^6)) = (2^2 × 3)/(2^2 × 5^2) = 3/25 = 0.12 The cube root of 0.001728 is 0.12.
Common Mistakes and How to Avoid Them in the Cube Root of 0.001728
Finding the cube root 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 perfect cube roots for non-perfect cube numbers.
Children always try to calculate an exact whole number for the cube root of numbers that are not perfect cubes. However, 0.001728 is a perfect cube, and its cube root is exactly 0.12. To avoid this error, memorize that some numbers, like 0.001728, have an exact cube root.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that the cube root can also be written in exponent form. For example: Forgetting that the cube root of 0.001728 is 0.001728^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
To avoid this, children should remember that the cube root of 0.001728 is the number they multiply by itself three times to get 0.001728, and not simply dividing 0.001728 by 3.
Mistake 4
Using approximation instead of exact methods
Instead of using the prime factorization method for perfect cubes, children might use approximation methods, which are unnecessary for perfect cubes. Remember that prime factorization is effective for perfect cubes like 0.001728.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps. For example, rounding the cube root of 0.001728 to 0.1 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result if necessary.
Cube Root of 0.001728 Examples:
Problem 1
Imagine you have a small box with a total volume of 0.001728 cubic meters. Find the length of one side of the box equal to its cube root.
Side of the box = ∛0.001728 = 0.12 meters
Explanation
To find the side of the box, we need to find the cube root of the given volume. Therefore, the side length of the box is exactly 0.12 meters.
Problem 2
A company manufactures 0.001728 cubic meters of material. Calculate the amount of material left after using 0.000728 cubic meters.
The amount of material left is 0.001 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 0.001728 - 0.000728 = 0.001 cubic meters.
Problem 3
A bottle holds 0.001728 cubic meters of volume. Another bottle holds a volume of 0.0008 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 0.002528 cubic meters.
Explanation
Explanation: Let’s add the volume of both bottles: 0.001728 + 0.0008 = 0.002528 cubic meters.
Problem 4
When the cube root of 0.001728 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 0.12 = 0.24 The cube of 0.24 = 0.013824
Explanation
When we multiply the cube root of 0.001728 by 2, the resulting number is 0.24, and its cube is 0.013824, showing the impact of exponential increase.
Problem 5
Find ∛(0.001 + 0.000728).
∛(0.001 + 0.000728) = ∛0.001728 = 0.12
Explanation
As shown in the question ∛(0.001 + 0.000728), we can simplify that by adding them. So, 0.001 + 0.000728 = 0.001728. Then we use this step: ∛0.001728 = 0.12 to get the answer.
FAQs on 0.001728 Cube Root
1.Can we find the Cube Root of 0.001728?
2.Why is the Cube Root of 0.001728 rational?
3.Is it possible to get the cube root of 0.001728 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 0.001728?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 0.001728?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 0.001728
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 or exact decimal. For example, 2 × 2 × 2 = 8, and 0.12 × 0.12 × 0.12 = 0.001728. 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 number. 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 finite decimal is rational. For example, the cube root of 0.001728 is rational because it is exactly 0.12.
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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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