103 LearnersLast updated on June 2nd, 2025
Cube of 448
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 448.
Cube of 448
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 448 can be written as 448³, which is the exponential form. Or it can also be written in arithmetic form as, 448 × 448 × 448.
How to Calculate the Value of Cube of 448
In order to check whether a number is a cube number or not, we can use the following three methods, such as 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.
448³ = 448 × 448 × 448.
Step 2: You get 89,479,552 as the answer.
Hence, the cube of 448 is 89,479,552.
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 448 into two parts.
Let a = 400 and b = 48, so a + b = 448
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 400³
3a²b = 3 × 400² × 48
3ab² = 3 × 400 × 48²
b³ = 48³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(400 + 48)³ = 400³ + 3 × 400² × 48 + 3 × 400 × 48² + 48³
448³ = 64,000,000 + 23,040,000 + 2,764,800 + 110,592 448³ = 89,479,392.
Step 5: Hence, the cube of 448 is 89,479,392.
Using a Calculator
To find the cube of 448 using a calculator, input the number 448 and use the cube function (if available) or multiply 448 × 448 × 448. This operation calculates the value of 448³, resulting in 89,479,392. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 4, followed by 4, then 8.
Step 3: If the calculator has a cube function, press it to calculate 448³.
Step 4: If there is no cube function on the calculator, simply multiply 448 three times manually.
Step 5: The calculator will display 89,479,392.
Tips and Tricks for the Cube of 448
- 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 448
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, 448 × 448 and not 448 × 448 × 448. Always remember that 448³ = 448 × 448 × 448.
Solved Examples on Cube of 448
Problem 1
What is the cube and cube root of 448?
The cube of 448 is 89,479,392 and the cube root of 448 is approximately 7.659.
Explanation
First, let’s find the cube of 448.
We know that 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 448³ = 89,479,392.
Next, we must find the cube root of 448.
We know that cube root of a number ‘x’, such that ∛x = y
Where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛448 ≈ 7.659.
Hence the cube of 448 is 89,479,392 and the cube root of 448 is approximately 7.659.
Problem 2
If the side length of the cube is 448 cm, what is the volume?
The volume is 89,479,392 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 448 for the side length: V = 448³ = 89,479,392 cm³.
Problem 3
How much larger is 448³ than 400³?
448³ – 400³ = 25,479,392.
Explanation
First find the cube of 448³, that is 89,479,392.
Next, find the cube of 400³, which is 64,000,000.
Now, find the difference between them using the subtraction method.
89,479,392 – 64,000,000 = 25,479,392.
Therefore, the 448³ is 25,479,392 larger than 400³.
Problem 4
If a cube with a side length of 448 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 448 cm is 89,479,392 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 448 means multiplying 448 by itself three times: 448 × 448 = 200,704, and then 200,704 × 448 = 89,479,392.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 89,479,392 cm³.
Problem 5
Estimate the cube 447.9 using the cube 448.
The cube of 447.9 is approximately 89,479,392.
Explanation
First, identify the cube of 448,
The cube of 448 is 448³ = 89,479,392.
Since 447.9 is only a tiny bit less than 448, the cube of 447.9 will be almost the same as the cube of 448.
The cube of 447.9 is approximately 89,479,392 because the difference between 447.9 and 448 is very small.
So, we can approximate the value as 89,479,392.
FAQs on Cube of 448
1.What are the perfect cubes up to 448?
2.How do you calculate 448³?
3.What is the meaning of 448³?
4.What is the cube root of 448?
5.Is 448 a perfect cube?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube of 448?
8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 448?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for Cube of 448
- 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 Formula: The formula to calculate the volume of a cube is V = Side³, where the side is the length of one edge of the cube.
- Perfect Cube: A number that can be expressed as the cube of an integer.
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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.
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