114 LearnersLast updated on May 30th, 2025
Cube of 405
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 405.
Cube of 405
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 405 can be written as 405³, which is the exponential form.
Or it can also be written in arithmetic form as, 405 × 405 × 405.
How to Calculate the Value of Cube of 405
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 (a3)
- 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. 405³ = 405 × 405 × 405
Step 2: You get 66,430,125 as the answer. Hence, the cube of 405 is 66,430,125.
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 405 into two parts, as and . Let a = 400 and b = 5, so a + b = 405
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 5 3ab² = 3 × 400 × 5² b³ = 5³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 5)³ = 400³ + 3 × 400² × 5 + 3 × 400 × 5² + 5³ 405³ = 64,000,000 + 2,400,000 + 24,000 + 125 405³ = 66,430,125
Step 5: Hence, the cube of 405 is 66,430,125.
Using a Calculator
To find the cube of 405 using a calculator, input the number 405 and use the cube function (if available) or multiply 405 × 405 × 405. This operation calculates the value of 405³, resulting in 66,430,125. 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 0 and 5
Step 3: If the calculator has a cube function, press it to calculate 405³.
Step 4: If there is no cube function on the calculator, simply multiply 405 three times manually.
Step 5: The calculator will display 66,430,125.
Tips and Tricks for the Cube of 405
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 405
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, 405 × 405 and not 405 × 405 × 405. Always remember that 405³ = 405 × 405 × 405.
Solved Examples on Cube of 405
Problem 1
What is the cube and cube root of 405?
The cube of 405 is 66,430,125 and the cube root of 405 is approximately 7.376.
Explanation
First, let’s find the cube of 405.
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 405³ = 66,430,125 Next, we must find the cube root of 405
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 ∛405 ≈ 7.376
Hence, the cube of 405 is 66,430,125 and the cube root of 405 is approximately 7.376.
Problem 2
If the side length of the cube is 405 cm, what is the volume?
The volume is 66,430,125 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 405 for the side length: V = 405³ = 66,430,125 cm³.
Problem 3
How much larger is 405³ than 400³?
405³ – 400³ = 2,430,125.
Explanation
First, find the cube of 405³, that is 66,430,125
Next, find the cube of 400³, which is 64,000,000
Now, find the difference between them using the subtraction method. 66,430,125 – 64,000,000 = 2,430,125
Therefore, 405³ is 2,430,125 larger than 400³.
Problem 4
If a cube with a side length of 405 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 405 cm is 66,430,125 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 405 means multiplying 405 by itself three times: 405 × 405 = 164,025, and then 164,025 × 405 = 66,430,125.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 66,430,125 cm³.
Problem 5
Estimate the cube of 404.9 using the cube of 405.
The cube of 404.9 is approximately 66,430,125.
Explanation
First, identify the cube of 405
The cube of 405 is 405³ = 66,430,125.
Since 404.9 is only a tiny bit less than 405, the cube of 404.9 will be almost the same as the cube of 405.
The cube of 404.9 is approximately 66,430,125 because the difference between 404.9 and 405 is very small.
So, we can approximate the value as 66,430,125.
FAQs on Cube of 405
1.What are the perfect cubes up to 405?
2.How do you calculate 405³?
3.What is the meaning of 405³?
4.What is the cube root of 405?
5.Is 405 a perfect cube?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube of 405?
8.How do technology and digital tools in Thailand support learning Algebra and Cube of 405?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube of 405
- 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.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Cube Root: The number 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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