119 LearnersLast updated on May 26th, 2025
Cube Root of 315
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 315 and explain the methods used.
What is the Cube Root of 315?
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, ∛315 is written as 315^(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 315, then y^3 can be 315. Since the cube root of 315 is not an exact value, we can write it as approximately 6.8752.
Finding the Cube Root of 315
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 315. 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 315 is not a perfect cube, we use Halley’s method.
Cube Root of 315 by Halley’s method
Let's find the cube root of 315 using Halley’s method
The formula is ∛a ≅ x((x^3 + 2a) / (2x^3 + a)) where:
a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 315;
x = 7
∛a ≅ 7((7^3 + 2 × 315) / (2 × 7^3 + 315)) ∛315 ≅ 7((343 + 2 × 315) / (2 × 343 + 315)) ∛315 ≅ 6.8752
The cube root of 315 is approximately 6.8752
Common Mistakes and How to Avoid Them in the Cube Root of 315
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 315, which are not perfect cubes.
For example: They assume that they would get an exact whole number for 315 like they get for 64 (since ∛64 = 4). To avoid this error, memorize that some numbers don't have a perfect cube root, that is, cube root 315 is approximately 6.8752.
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 315 is 315^(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 315 is to divide 315 by 3.
For example: Mistakenly assume 315/3. To avoid this, children should remember that the cube root of 315 is the number they multiply by itself three times to get 315.
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 315 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 315 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 315 to 6.9 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result.
Cube Root of 315 Examples:
Problem 1
Imagine you have a cube-shaped garden plot that has a total volume of 315 cubic meters. Find the length of one side of the plot equal to its cube root.
Side of the cube = ∛315 = 6.8752 meters
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 6.8752 meters.
Problem 2
A company receives 315 cubic meters of soil. Calculate the amount of soil left after using 100 cubic meters.
The amount of soil left is 215 cubic meters.
Explanation
To find the remaining soil, we need to subtract the used soil from the total amount: 315 - 100 = 215 cubic meters.
Problem 3
A tank holds 315 cubic meters of water. Another tank holds a volume of 85 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 400 cubic meters.
Explanation
Explanation: Let’s add the volume of both tanks: 315 + 85 = 400 cubic meters.
Problem 4
When the cube root of 315 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 6.8752 = 20.6256 The cube of 20.6256 = approximately 8,784.53
Explanation
When we multiply the cube root of 315 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(150 + 165).
∛(150 + 165) = ∛315 ≈ 6.8752
Explanation
As shown in the question ∛(150 + 165), we can simplify that by adding them.
So, 150 + 165 = 315.
Then we use this step: ∛315 ≈ 6.8752 to get the answer.
FAQs on 315 Cube Root
1.Can we find the Cube Root of 315?
2.Why is Cube Root of 315 irrational?
3.Is it possible to get the cube root of 315 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 Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube Root of 315?
8.How do technology and digital tools in Philippines support learning Algebra and Cube Root of 315?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube Root of 315
- 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 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 (∛).
- Irrational number: The numbers that cannot be put in fractional forms are irrational. For example, the cube root of 315 is irrational because its decimal form goes on continuously without repeating the numbers.
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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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