100 LearnersLast updated on June 2nd, 2025
Cube of 425
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is often used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 425.
Cube of 425
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 multiplying a negative number by itself three times results in a negative number.
The cube of 425 can be written as 425³, which is the exponential form.
Or it can also be written in arithmetic form as 425 × 425 × 425.
How to Calculate the Value of Cube of 425
In order to check whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help you cube numbers faster and easier without getting 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 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. 425³ = 425 × 425 × 425
Step 2: You get 76,765,625 as the answer. Hence, the cube of 425 is 76,765,625.
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 425 into two parts, as 400 and 25. Let a = 400 and b = 25, so a + b = 425
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 25 3ab² = 3 × 400 × 25² b³ = 25³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 25)³ = 400³ + 3 × 400² × 25 + 3 × 400 × 25² + 25³ 425³ = 64,000,000 + 12,000,000 + 750,000 + 15,625 425³ = 76,765,625
Step 5: Hence, the cube of 425 is 76,765,625.
Using a Calculator
To find the cube of 425 using a calculator, input the number 425 and use the cube function (if available) or multiply 425 × 425 × 425. This operation calculates the value of 425³, resulting in 76,765,625. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 425
Step 3: If the calculator has a cube function, press it to calculate 425³.
Step 4: If there is no cube function on the calculator, simply multiply 425 three times manually.
Step 5: The calculator will display 76,765,625.
Tips and Tricks for the Cube of 425
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 425
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might happen:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice. That is, 425 × 425 and not 425 × 425 × 425. Always remember that 425³ = 425 × 425 × 425.
Solved Examples on Cube of 425
Problem 1
What is the cube and cube root of 425?
The cube of 425 is 76,765,625 and the cube root of 425 is approximately 7.5.
Explanation
First, let’s find the cube of 425.
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 425³ = 76,765,625.
Next, we must find the cube root of 425.
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 ∛425 ≈ 7.5.
Hence, the cube of 425 is 76,765,625, and the cube root of 425 is approximately 7.5.
Problem 2
If the side length of the cube is 425 cm, what is the volume?
The volume is 76,765,625 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 425 for the side length: V = 425³ = 76,765,625 cm³.
Problem 3
How much larger is 425³ than 400³?
425³ – 400³ = 12,765,625.
Explanation
First, find the cube of 425, which is 76,765,625.
Next, find the cube of 400, which is 64,000,000.
Now, find the difference between them using the subtraction method. 76,765,625 – 64,000,000 = 12,765,625.
Therefore, 425³ is 12,765,625 larger than 400³.
Problem 4
If a cube with a side length of 425 cm is compared to a cube with a side length of 25 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 425 cm is 76,765,625 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 425 means multiplying 425 by itself three times: 425 × 425 = 180,625, and then 180,625 × 425 = 76,765,625.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 76,765,625 cm³.
Problem 5
Estimate the cube 424.9 using the cube 425.
The cube of 424.9 is approximately 76,765,625.
Explanation
First, identify the cube of 425,
The cube of 425 is 425³ = 76,765,625.
Since 424.9 is only a tiny bit less than 425, the cube of 424.9 will be almost the same as the cube of 425.
The cube of 424.9 is approximately 76,765,625 because the difference between 424.9 and 425 is very small.
So, we can approximate the value as 76,765,625.
FAQs on Cube of 425
1.What are the perfect cubes up to 425?
2.How do you calculate 425³?
3.What is the meaning of 425³?
4.What is the cube root of 425?
5.Is 425 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 425?
8.How do technology and digital tools in United States support learning Algebra and Cube of 425?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 425
- 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.
- Cube Root: The number that produces a specified quantity when multiplied by itself three times.
- Perfect Cube: A number that is the cube of an integer. For example, 8 is a perfect cube because it is 2³.
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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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