103 LearnersLast updated on May 26th, 2025
Cube Root of 522
A number we multiply by itself three times to get the original number is its cube root. The cube root has various applications in real life, such as determining the dimensions of cube-shaped objects and designing structures. We will now find the cube root of 522 and explain the methods used.
What is the Cube Root of 522?
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, ∛522 is written as 522(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 522, then y3 can be 522. Since the cube root of 522 is not an exact value, we can write it as approximately 8.0591.
Finding the Cube Root of 522
Finding the cube root of a number involves identifying the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of 522. The common methods we use to find the cube root are:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a non-perfect cube, we often follow Halley’s method. Since 522 is not a perfect cube, we use Halley’s method.
Cube Root of 522 by Halley’s Method
Let's find the cube root of 522 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 = 522; x = 8
∛a ≅ 8((83 + 2 × 522) / (2 × 83 + 522))
∛522 ≅ 8((512 + 2 × 522) / (2 × 512 + 522))
∛522 ≅ 8.0591
The cube root of 522 is approximately 8.0591.
Common Mistakes and How to Avoid Them in the Cube Root of 522
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 students commonly make and ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers like 522, which are not perfect cubes. For example, they might assume that they would get an exact whole number for 522 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, the cube root of 522 is approximately 8.0591.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that a cube root can also be written in exponent form. For example, forgetting that the cube root of 522 is 522(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
Some might mistakenly assume that finding the cube root of 522 involves dividing 522 by 3. To avoid this, remember that the cube root of 522 is the number that you multiply by itself three times to achieve 522.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, children might use prime factorization. For example, they might try to find the cube root of 522 by breaking it down into its prime factors.
Remember that prime factorization is useful for analyzing a number's factors but not for non-perfect cubes. Since 522 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 subsequent steps. For example, rounding the cube root of 522 to 8.1 too early in the calculation.
To avoid this, ensure the whole calculation is done, then round the final result.
Cube Root of 522 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 522 cubic centimeters. Find the length of one side of the cube, which is equal to its cube root.
Side of the cube = ∛522 ≈ 8.06 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 8.06 units.
Problem 2
A company manufactures 522 cubic meters of material. Calculate the amount of material left after using 150 cubic meters.
The amount of material left is 372 cubic meters.
Explanation
To find the remaining material,
we need to subtract the used material from the total amount:
522 - 150 = 372 cubic meters.
Problem 3
A bottle holds 522 cubic meters of volume. Another bottle holds a volume of 50 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 572 cubic meters.
Explanation
Let’s add the volume of both bottles:
522 + 50 = 572 cubic meters.
Problem 4
When the cube root of 522 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 8.06 = 16.12
The cube of 16.12 = 4187.5
Explanation
When we multiply the cube root of 522 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(250 + 272).
∛(250 + 272) = ∛522 ≈ 8.06
Explanation
As shown in the question ∛(250 + 272), we can simplify that by adding them.
So, 250 + 272 = 522.
Then use this step: ∛522 ≈ 8.06 to get the answer.
FAQs on Cube Root of 522
1.Can we find the Cube Root of 522?
2.Why is the Cube Root of 522 irrational?
3.Is it possible to get the cube root of 522 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 522?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube Root of 522?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube Root of 522
- 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, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
- Exponent: The exponent form of the number indicates how many times a number can be multiplied by itself. In 522(1/3), ⅓ is the exponent that denotes the cube root of 522.
- Radical sign: The symbol used to represent a root is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a fraction are irrational. For example, the cube root of 522 is irrational because its decimal form goes on continuously without repeating.
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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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