100 LearnersLast updated on June 2nd, 2025
Cube of 458
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 458.
Cube of 458
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 458 can be written as 458³, which is the exponential form. Or it can also be written in arithmetic form as 458 × 458 × 458.
How to Calculate the Value of Cube of 458
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.
458³ = 458 × 458 × 458
Step 2: You get 96,036,872 as the answer.
Hence, the cube of 458 is 96,036,872.
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 458 into two parts.
Let a = 450 and b = 8, so a + b = 458.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 450³
3a²b = 3 × 450² × 8
3ab² = 3 × 450 × 8²
b³ = 8³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(450 + 8)³ = 450³ + 3 × 450² × 8 + 3 × 450 × 8² + 8³
458³ = 91,125,000 + 4,860,000 + 108,000 + 512
458³ = 96,036,872
Step 5: Hence, the cube of 458 is 96,036,872.
Using a Calculator
To find the cube of 458 using a calculator, input the number 458 and use the cube function (if available) or multiply 458 × 458 × 458. This operation calculates the value of 458³, resulting in 96,036,872. 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 5 and 8.
Step 3: If the calculator has a cube function, press it to calculate 458³.
Step 4: If there is no cube function on the calculator, simply multiply 458 three times manually.
Step 5: The calculator will display 96,036,872.
Tips and Tricks for the Cube of 458
- 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 458
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, 458 × 458 and not 458 × 458 × 458. Always remember that 458³ = 458 × 458 × 458.
Solved Examples on Cube of 458
Problem 1
What is the cube and cube root of 458?
The cube of 458 is 96,036,872 and the cube root of 458 is approximately 7.72.
Explanation
First, let’s find the cube of 458.
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 458³ = 96,036,872 Next, we must find the cube root of 458.
We know that the 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 ∛458 ≈ 7.72.
Hence the cube of 458 is 96,036,872 and the cube root of 458 is approximately 7.72.
Problem 2
If the side length of the cube is 458 cm, what is the volume?
The volume is 96,036,872 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 458 for the side length: V = 458³ = 96,036,872 cm³.
Problem 3
How much larger is 458³ than 350³?
458³ – 350³ = 66,623,872.
Explanation
First, find the cube of 458³, which is 96,036,872.
Next, find the cube of 350³, which is 29,413,000.
Now, find the difference between them using the subtraction method.
96,036,872 – 29,413,000 = 66,623,872.
Therefore, 458³ is 66,623,872 larger than 350³.
Problem 4
If a cube with a side length of 458 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 458 cm is 95,536,872 cm³ larger than the smaller cube.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 458 means multiplying 458 by itself three times: 458 × 458 = 209,764, and then 209,764 × 458 = 96,036,872.
The volume of the cube with a side length of 100 cm is 100³ = 1,000,000 cm³.
The difference in volume is 96,036,872 – 1,000,000 = 95,036,872 cm³.
Therefore, the volume of the larger cube is 95,036,872 cm³ larger.
Problem 5
Estimate the cube 457.9 using the cube 458.
The cube of 457.9 is approximately 96,036,872.
Explanation
First, identify the cube of 458,
The cube of 458 is 458³ = 96,036,872.
Since 457.9 is only a tiny bit less than 458, the cube of 457.9 will be almost the same as the cube of 458.
The cube of 457.9 is approximately 96,036,872 because the difference between 457.9 and 458 is very small.
So, we can approximate the value as 96,036,872.
FAQs on Cube of 458
1.What are the perfect cubes up to 458?
2.How do you calculate 458³?
3.What is the meaning of 458³?
4.What is the cube root of 458?
5.Is 458 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 458?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 458?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 458
- 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 to obtain the cube of that 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.
- Volume of a Cube: The amount of space enclosed within a cube, calculated as the cube of the side length.
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Jaskaran Singh Saluja
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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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