126 LearnersLast updated on May 26th, 2025
Cube Root of 423
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 423 and explain the methods used.
What is the Cube Root of 423?
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, ∛423 is written as 423(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 423, then y3 can be 423. Since the cube root of 423 is not an exact value, so we can write it as approximately 7.498.
Finding the Cube Root of 423
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 423. 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 non-perfect number, we often follow Halley’s method. Since 423 is not a perfect cube, we use Halley’s method.
Cube Root of 423 by Halley’s method
Let's find the cube root of 423 using Halley’s method.
The formula is ∛a ≅ x((x3 + 2a) / (2x3 + a))
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 423; x = 7
∛a ≅ 7((73 + 2 × 423) / (2 × 73 + 423))
∛423 ≅ 7((343 + 2 × 423) / (2 × 343 + 423))
∛423 ≅ 7.498
The cube root of 423 is approximately 7.498.
Common Mistakes and How to Avoid Them in the Cube Root of 423
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 423, which are not perfect cubes. For example, they assume that they would get an exact whole number for 423 like they get for 512 (since ∛512 = 8). To avoid this error, memorize that some numbers don't have a perfect cube root, that is, cube root of 423 is approximately 7.498.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that cube root can also be written in exponent form. For example, forgetting that the cube root of 423 is 423(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
Assuming the cube root of 423 is to divide 423 by 3. For example, mistakenly assume ∛423 = 423/3. To avoid this, children should remember that the cube root of 423 is the number they multiply by itself three times to get 423.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, children end up using prime factorization. For example, they might try to find cube root 423 by breaking it down into its prime factors. Remember that prime factorization can help analyze a number's factors, but it's not the best method for non-perfect cubes. Since 423 is a non-perfect cube, you can use either the approximation method or Halley’s method.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps. For example, we might round the cube root of 423 to 7.5 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result.
Cube Root of 423 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of 423 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛423 = 7.498 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 approximately 7.498 units.
Problem 2
A company manufactures 423 cubic meters of material. Calculate the amount of material left after using 100 cubic meters.
The amount of material left is 323 cubic meters.
Explanation
To find the remaining material,
we need to subtract the used material from the total amount:
423 - 100 = 323 cubic meters.
Problem 3
A tank holds 423 cubic meters of water. Another tank holds a volume of 77 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 500 cubic meters.
Explanation
Let’s add the volume of both tanks:
423 + 77 = 500 cubic meters.
Problem 4
When the cube root of 423 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 7.498 = 22.494
The cube of 22.494 = 11,360.6
Explanation
When we multiply the cube root of 423 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(200 + 223).
∛(200 + 223) = ∛423 ≈ 7.498
Explanation
As shown in the question ∛(200 + 223), we can simplify that by adding them.
So, 200 + 223 = 423.
Then we use this step: ∛423 ≈ 7.498 to get the answer.
FAQs on 423 Cube Root
1.Can we find the Cube Root of 423?
2.Why is Cube Root of 423 irrational?
3.Is it possible to get the cube root of 423 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 Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Cube Root of 423?
8.How do technology and digital tools in Oman support learning Algebra and Cube Root of 423?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube Root of 423
- 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 423(1/3), ⅓ is the exponent which denotes the cube root of 423.
- Radical sign: The symbol that is used to represent a root which is expressed as (∛).
- Irrational number: The numbers that cannot be put in fractional forms are irrational. For example, the cube root of 423 is irrational because its decimal form goes on continuously without repeating the numbers.
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Jaskaran Singh Saluja
About the Author
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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: He loves to play the quiz with kids through algebra to make kids love it.
