101 LearnersLast updated on June 2nd, 2025
Cube of 667
When a number is multiplied by itself thrice, the resultant number is called the cube of that number. Cubing is often used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 667.
Cube of 667
A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times. When you cube a positive number, the result is always positive. When you cube a negative number, the result is always negative. This is because a negative number multiplied by itself three times results in a negative number.
The cube of 667 can be written as 667³, which is the exponential form. Or it can also be written in arithmetic form as 667 × 667 × 667.
How to Calculate the Value of Cube of 667
To determine whether a number is a cube number or not, we can use three methods: the multiplication method, a factor formula (a³), or by using a calculator. These methods will help in cubing numbers faster and easier without feeling confused or stuck while evaluating the answers.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number. 667³ = 667 × 667 × 667
Step 2: Calculate the result. The cube of 667 is 296,344,963.
Using a Formula (a³)
The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.
Step 1: Split the number 667 into two parts. Let a = 660 and b = 7, so a + b = 667
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 660³
3a²b = 3 × 660² × 7
3ab² = 3 × 660 × 7²
b³ = 7³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(660 + 7)³ = 660³ + 3 × 660² × 7 + 3 × 660 × 7² + 7³
667³ = 287,496,000 + 92,400 + 9,702 + 343
667³ = 296,344,963
Step 5: Hence, the cube of 667 is 296,344,963.
Using a Calculator
To find the cube of 667 using a calculator, input the number 667 and use the cube function (if available) or multiply 667 × 667 × 667. This operation calculates the value of 667³, resulting in 296,344,963. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6 followed by 6 and then 7
Step 3: If the calculator has a cube function, press it to calculate 667³.
Step 4: If there is no cube function on the calculator, simply multiply 667 three times manually.
Step 5: The calculator will display 296,344,963.
Tips and Tricks for the Cube of 667
- The cube of any even number is always even, while the cube of any odd number is always odd.
- The product of two or more perfect cube numbers is always a perfect cube.
- A perfect cube can always be expressed as the product of three identical groups of equal prime factors.
Common Mistakes to Avoid When Calculating the Cube of 667
There are some typical errors that people might make during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice. That is, 667 × 667 and not 667 × 667 × 667. Always remember that 667³ = 667 × 667 × 667.
Solved Examples on Cube of 667
Problem 1
What is the cube and cube root of 667?
The cube of 667 is 296,344,963, and the cube root of 667 is approximately 8.73.
Explanation
First, let’s find the cube of 667.
We know that the cube of a number is such that x³ = y, where x is the given number and y is the cubed value of that number.
So, we get 667³ = 296,344,963.
Next, we must find the cube root of 667. We know that the cube root of a number 'x' is such that ∛x = y, where 'x' is the given number and y is the cube root value of the number.
So, we get ∛667 ≈ 8.73.
Hence, the cube of 667 is 296,344,963, and the cube root of 667 is approximately 8.73.
Problem 2
If the side length of a cube is 667 cm, what is the volume?
The volume is 296,344,963 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 667 for the side length: V = 667³ = 296,344,963 cm³.
Problem 3
How much larger is 667³ than 660³?
667³ – 660³ = 2,496,963.
Explanation
First, find the cube of 667, which is 296,344,963.
Next, find the cube of 660, which is 287,496,000.
Now, find the difference between them using the subtraction method.
296,344,963 – 287,496,000 = 2,496,963.
Therefore, 667³ is 2,496,963 larger than 660³.
Problem 4
If a cube with a side length of 667 cm is compared to a cube with a side length of 7 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 667 cm is 296,344,963 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 667 means multiplying 667 by itself three times: 667 × 667 = 444,889, and then 444,889 × 667 = 296,344,963.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 296,344,963 cm³.
Problem 5
Estimate the cube of 666.9 using the cube of 667.
The cube of 666.9 is approximately 296,344,963.
Explanation
First, identify the cube of 667.
The cube of 667 is 667³ = 296,344,963. Since 666.9 is only a tiny bit less than 667, the cube of 666.9 will be almost the same as the cube of 667.
The cube of 666.9 is approximately 296,344,963 because the difference between 666.9 and 667 is very small.
So, we can approximate the value as 296,344,963.
FAQs on Cube of 667
1.What are the perfect cubes up to 667?
2.How do you calculate 667³?
3.What is the meaning of 667³?
4.What is the cube root of 667?
5.Is 667 a perfect cube?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Cube of 667?
8.How do technology and digital tools in Canada support learning Algebra and Cube of 667?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube of 667
- Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
- Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
- Exponential Form: A way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Volume of a Cube: The amount of space inside a cube, calculated as the side length raised to the third power.
Explore More algebra
Previous to Cube of 667
Next to Cube of 667
About BrightChamps in Canada
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.
