102 LearnersLast updated on June 2nd, 2025
Cube of 648
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 648.
Cube of 648
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 by itself three times results in a negative number.
The cube of 648 can be written as 648³, which is the exponential form. Or it can also be written in arithmetic form as 648 × 648 × 648.
How to Calculate the Value of Cube of 648
In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube the 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. 648³ = 648 × 648 × 648
Step 2: You get 272,097,792 as the answer. Hence, the cube of 648 is 272,097,792.
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 648 into two parts, as 640 and 8. Let a = 640 and b = 8, so a + b = 648
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 640³
3a²b = 3 × 640² × 8
3ab² = 3 × 640 × 8²
b³ = 8³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(640 + 8)³ = 640³ + 3 × 640² × 8 + 3 × 640 × 8² + 8³
648³ = 262,144,000 + 98,304,000 + 122,880 + 512
648³ = 272,097,792
Step 5: Hence, the cube of 648 is 272,097,792.
Using a Calculator
To find the cube of 648 using a calculator, input the number 648 and use the cube function (if available) or multiply 648 × 648 × 648. This operation calculates the value of 648³, resulting in 272,097,792. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 648
Step 3: If the calculator has a cube function, press it to calculate 648³.
Step 4: If there is no cube function on the calculator, simply multiply 648 three times manually.
Step 5: The calculator will display 272,097,792.
Tips and Tricks for the Cube of 648
- 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 648
There are some typical errors that kids might make during the process of cubing a number. Let us take a look at five of the major mistakes that kids might make:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 648 × 648 and not 648 × 648 × 648. Always remember that 648³ = 648 × 648 × 648.
Solved Examples on Cube of 648
Problem 1
What is the cube and cube root of 648?
The cube of 648 is 272,097,792, and the cube root of 648 is approximately 8.654.
Explanation
First, let’s find the cube of 648.
We know that the cube of a number, such that x³ = y. Where x is the given number, and y is the cubed value of that number.
So, we get 648³ = 272,097,792.
Next, we must find the cube root of 648. We know that the cube root of a number ‘x’, such that ³√x = y. Where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ³√648 ≈ 8.654.
Hence, the cube of 648 is 272,097,792, and the cube root of 648 is approximately 8.654.
Problem 2
If the side length of the cube is 648 cm, what is the volume?
The volume is 272,097,792 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 648 for the side length: V = 648³ = 272,097,792 cm³.
Problem 3
How much larger is 648³ than 640³?
648³ – 640³ = 9,953,792.
Explanation
First find the cube of 648³, which is 272,097,792.
Next, find the cube of 640³, which is 262,144,000.
Now, find the difference between them using the subtraction method. 272,097,792 – 262,144,000 = 9,953,792.
Therefore, 648³ is 9,953,792 larger than 640³.
Problem 4
If a cube with a side length of 648 cm is compared to a cube with a side length of 8 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 648 cm is 272,097,792 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 648 means multiplying 648 by itself three times: 648 × 648 = 419,904, and then 419,904 × 648 = 272,097,792.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 272,097,792 cm³.
Problem 5
Estimate the cube of 647.9 using the cube of 648.
The cube of 647.9 is approximately 272,097,792.
Explanation
First, identify the cube of 648.
The cube of 648 is 648³ = 272,097,792.
Since 647.9 is only a tiny bit less than 648, the cube of 647.9 will be almost the same as the cube of 648.
The cube of 647.9 is approximately 272,097,792 because the difference between 647.9 and 648 is very small.
So, we can approximate the value as 272,097,792.
FAQs on Cube of 648
1.What are the perfect cubes up to 648?
2.How do you calculate 648³?
3.What is the meaning of 648³?
4.What is the cube root of 648?
5.Is 648 a perfect cube?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 648?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 648?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube of 648
- Binomial Formula: It is 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: It is 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.
- Volume: The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great. In this context, it refers to the space inside a cube.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8.
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About BrightChamps in Saudi Arabia
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.
