114 LearnersLast updated on May 30th, 2025
Cube of 548
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is useful when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 548.
Cube of 548
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 548 can be written as 548³, which is the exponential form.
Or it can also be written in arithmetic form as 548 × 548 × 548.
How to Calculate the Value of Cube of 548
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 you cube numbers faster and easier without feeling confused or stuck while evaluating the answers.
- By Multiplication Method
- Using a Formula (a3)
- Using a Calculator
By Multiplication Method
The multiplication method is a process in mathematics used to find the product of 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. 548³ = 548 × 548 × 548
Step 2: Calculate the product. By computing, you get 164,303,792 as the answer. Hence, the cube of 548 is 164,303,792.
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 548 into two parts, such as 500 and 48. Let a = 500 and b = 48, so a + b = 548
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ 3a²b = 3 × 500² × 48 3ab² = 3 × 500 × 48² b³ = 48³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (500 + 48)³ = 500³ + 3 × 500² × 48 + 3 × 500 × 48² + 48³ 548³ = 125,000,000 + 36,000,000 + 3,456,000 + 110,592 548³ = 164,303,792
Step 5: Hence, the cube of 548 is 164,303,792.
Using a Calculator
To find the cube of 548 using a calculator, input the number 548 and use the cube function (if available) or multiply 548 × 548 × 548. This operation calculates the value of 548³, resulting in 164,303,792. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 5, 4, and 8 in sequence.
Step 3: If the calculator has a cube function, press it to calculate 548³.
Step 4: If there is no cube function on the calculator, simply multiply 548 three times manually.
Step 5: The calculator will display 164,303,792.
Tips and Tricks for the Cube of 548
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 548
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five major mistakes:
Mistake 1
Incorrect Multiplication
Multiplying the numbers only twice, such as 548 × 548 and not 548 × 548 × 548. Always remember that 548³ = 548 × 548 × 548.
Solved Examples on Cube of 548
Problem 1
What is the cube and cube root of 548?
The cube of 548 is 164,303,792 and the cube root of 548 is approximately 8.184.
Explanation
First, let’s find the cube of 548.
The cube of a number is calculated as x³ = y. So, 548³ = 164,303,792.
Next, find the cube root of 548. The cube root of a number 'x' is calculated as ³√x = y.
So, ³√548 ≈ 8.184.
Hence, the cube of 548 is 164,303,792 and the cube root of 548 is approximately 8.184.
Problem 2
If the side length of the cube is 548 cm, what is the volume?
The volume is 164,303,792 cm³.
Explanation
Use the volume formula for a cube V = side³.
Substitute 548 for the side length: V = 548³ = 164,303,792 cm³.
Problem 3
How much larger is 548³ than 500³?
548³ – 500³ = 39,303,792.
Explanation
First, find the cube of 548, which is 164,303,792.
Next, find the cube of 500, which is 125,000,000.
Now, find the difference between them using the subtraction method. 164,303,792 – 125,000,000 = 39,303,792.
Therefore, 548³ is 39,303,792 larger than 500³.
Problem 4
If a cube with a side length of 548 cm is compared to a cube with a side length of 48 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 548 cm is 164,303,792 cm³.
Explanation
To find its volume, multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 548 means multiplying 548 by itself three times. 548 × 548 = 300,304, and then 300,304 × 548 = 164,303,792.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 164,303,792 cm³.
Problem 5
Estimate the cube 547 using the cube 548.
The cube of 547 is approximately 164,303,792.
Explanation
First, identify the cube of 548, The cube of 548 is 548³ = 164,303,792.
Since 547 is only slightly less than 548, the cube of 547 will be almost the same as the cube of 548.
The cube of 547 is approximately 164,303,792 because the difference between 547 and 548 is very small.
So, we can approximate the value as 164,303,792.
FAQs on Cube of 548
1.What are the perfect cubes up to 548?
2.How do you calculate 548³?
3.What is the meaning of 548³?
4.What is the cube root of 548?
5.Is 548 a perfect cube?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 548?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 548?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 548
- 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, which equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because it is 3³.
- Volume of a Cube: The amount of space enclosed within a cube, calculated as side length cubed (side³).
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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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