101 LearnersLast updated on May 26th, 2025
Cube of 496
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 cubes of 496.
Cube of 496
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 496 can be written as 496³, which is the exponential form. Or it can also be written in arithmetic form as, 496 × 496 × 496.
How to Calculate the Value of Cube of 496
In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, 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. 496³ = 496 × 496 × 496
Step 2: Calculate the product to get the answer. Hence, the cube of 496 is 122,036,224.
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 496 into two parts, as a and b. Let a = 400 and b = 96, so a + b = 496.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term: a³ = 400³ 3a²b = 3 × 400² × 96 3ab² = 3 × 400 × 96² b³ = 96³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 96)³ = 400³ + 3 × 400² × 96 + 3 × 400 × 96² + 96³ 496³ = 64,000,000 + 46,080,000 + 11,059,200 + 884,736 496³ = 122,036,224
Step 5: Hence, the cube of 496 is 122,036,224.
Using a Calculator
To find the cube of 496 using a calculator, input the number 496 and use the cube function (if available) or multiply 496 × 496 × 496. This operation calculates the value of 496³, resulting in 122,036,224. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 496.
Step 3: If the calculator has a cube function, press it to calculate 496³.
Step 4: If there is no cube function on the calculator, simply multiply 496 three times manually.
Step 5: The calculator will display 122,036,224.
Tips and Tricks for the Cube of 496
- 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 496
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, 496 × 496 and not 496 × 496 × 496. Always remember that 496³ = 496 × 496 × 496.
Solved Examples on Cube of 496
Problem 1
What is the cube and cube root of 496?
The cube of 496 is 122,036,224 and the cube root of 496 is approximately 7.937.
Explanation
First, let’s find the cube of 496.
We know that the cube of a number is calculated as x³ = y, where x is the given number, and y is the cubed value of that number.
So, we get 496³ = 122,036,224.
Next, we must find the cube root of 496. We know that the cube root of a number ‘x’ is calculated as ∛x = y, where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛496 ≈ 7.937. Hence, the cube of 496 is 122,036,224 and the cube root of 496 is approximately 7.937.
Problem 2
If the side length of the cube is 496 cm, what is the volume?
The volume is 122,036,224 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 496 for the side length: V = 496³ = 122,036,224 cm³.
Problem 3
How much larger is 496³ than 400³?
496³ - 400³ = 58,036,224.
Explanation
First, find the cube of 496, which is 122,036,224.
Next, find the cube of 400, which is 64,000,000.
Now, find the difference between them using the subtraction method.
122,036,224 - 64,000,000 = 58,036,224. Therefore, 496³ is 58,036,224 larger than 400³.
Problem 4
If a cube with a side length of 496 cm is compared to a cube with a side length of 50 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 496 cm is 122,036,224 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 496 means multiplying 496 by itself three times: 496 × 496 = 246,016, and then 246,016 × 496 = 122,036,224.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 122,036,224 cm³.
Problem 5
Estimate the cube 495 using the cube 496.
The cube of 495 is approximately 122,036,224.
Explanation
First, identify the cube of 496, The cube of 496 is 496³ = 122,036,224.
Since 495 is only slightly less than 496, the cube of 495 will be almost the same as the cube of 496.
The cube of 495 is approximately 122,036,224 because the difference between 495 and 496 is very small.
So, we can approximate the value as 122,036,224.
FAQs on Cube of 496
1.What are the perfect cubes up to 496?
2.How do you calculate 496³?
3.What is the meaning of 496³?
4.What is the cube root of 496?
5.Is 496 a perfect cube?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Cube of 496?
8.How do technology and digital tools in Qatar support learning Algebra and Cube of 496?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Cube of 496
- 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 product of three equal integers.
- Cube Root: A value that, when multiplied by itself three times, gives the original number.
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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
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