115 LearnersLast updated on May 26th, 2025
Cube Root of 667
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 667 and explain the methods used.
What is the Cube Root of 667?
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, ∛667 is written as 667(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 667, then y3 can be 667. Since the cube root of 667 is not an exact value, we can write it as approximately 8.7799.
Finding the Cube Root of 667
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 667. 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 667 is not a perfect cube, we use Halley’s method.
Cube Root of 667 by Halley’s Method
Let's find the cube root of 667 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 root
Substituting, a = 667; x = 8
∛a ≅ 8((83 + 2 × 667) / (2 × 83 + 667))
∛667 ≅ 8((512 + 2 × 667) / (2 × 512 + 667))
∛667 ≅ 8.7799
The cube root of 667 is approximately 8.7799.
Common Mistakes and How to Avoid Them in the Cube Root of 667
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 667, which are not perfect cubes.
For example: They assume that they would get an exact whole number for 667 like they get for 512(since 512 = 83). To avoid this error, memorize that some numbers don't have a perfect cube root, that is, the cube root of 667 is approximately 8.7799.
Cube Root of 667 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 667 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛667 ≈ 8.7799 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 8.7799 units.
Problem 2
A company manufactures 667 cubic meters of a product. Calculate the amount remaining after using 245 cubic meters.
The amount of product left is 422 cubic meters.
Explanation
To find the remaining product, we need to subtract the used product from the total amount: 667 - 245 = 422 cubic meters.
Problem 3
A tank holds 667 cubic meters of water. Another tank holds a volume of 120 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 787 cubic meters.
Explanation
Explanation: Let’s add the volume of both tanks: 667 + 120 = 787 cubic meters.
Problem 4
When the cube root of 667 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 8.7799 = 26.3397 The cube of 26.3397 ≈ 18,254.5
Explanation
When we multiply the cube root of 667 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(300 + 367).
∛(300 + 367) = ∛667 ≈ 8.7799
Explanation
As shown in the question ∛(300 + 367), we can simplify that by adding them.
So, 300 + 367 = 667. Then we use this step: ∛667 ≈ 8.7799 to get the answer.
FAQs on 667 Cube Root
1.Can we find the Cube Root of 667?
2.Why is the Cube Root of 667 irrational?
3.Is it possible to get the cube root of 667 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?
Important Glossaries for Cube Root of 667
- 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 is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as fractions are irrational. For example, the cube root of 667 is irrational because its decimal form goes on continuously without repeating.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
