100 LearnersLast updated on June 6th, 2025
Cube of 807
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 807.
Cube of 807
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 807 can be written as 807³, which is the exponential form. Or it can also be written in arithmetic form as, 807 × 807 × 807.
How to Calculate the Value of Cube of 807
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 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. 807³ = 807 × 807 × 807
Step 2: Calculate the product to get the answer. Hence, the cube of 807 is 525,344,343.
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 807 into two parts. Let a = 800 and b = 7, so a + b = 807
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 800³
3a²b = 3 × 800² × 7
3ab² = 3 × 800 × 7²
b³ = 7³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(800 + 7)³ = 800³ + 3 × 800² × 7 + 3 × 800 × 7² + 7³
807³ = 512,000,000 + 134,400 + 11,760 + 343
807³ = 525,344,343
Step 5: Hence, the cube of 807 is 525,344,343.
Using a Calculator
To find the cube of 807 using a calculator, input the number 807 and use the cube function (if available) or multiply 807 × 807 × 807. This operation calculates the value of 807³, resulting in 525,344,343. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 8 followed by 0 and 7
Step 3: If the calculator has a cube function, press it to calculate 807³.
Step 4: If there is no cube function on the calculator, simply multiply 807 three times manually.
Step 5: The calculator will display 525,344,343.
Tips and Tricks for the Cube of 807
- 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 807
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, 807 × 807 and not 807 × 807 × 807. Always remember that 807³ = 807 × 807 × 807.
Solved Examples on Cube of 807
Problem 1
What is the cube and cube root of 807?
The cube of 807 is 525,344,343 and the cube root of 807 is approximately 9.308.
Explanation
First, let’s find the cube of 807.
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 807³ = 525,344,343
Next, we must find the cube root of 807 We know that the cube root of a number x, such that ³√x = y Where x is the given number, and y is the cube root value of the number
So, we get ³√807 ≈ 9.308
Hence the cube of 807 is 525,344,343 and the cube root of 807 is approximately 9.308.
Problem 2
If the side length of the cube is 807 cm, what is the volume?
The volume is 525,344,343 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 807 for the side length: V = 807³ = 525,344,343 cm³.
Problem 3
How much larger is 807³ than 407³?
807³ – 407³ = 515,554,343.
Explanation
First, find the cube of 807, that is 525,344,343
Next, find the cube of 407, which is 9,790,000
Now, find the difference between them using the subtraction method. 525,344,343 – 9,790,000 = 515,554,343
Therefore, the 807³ is 515,554,343 larger than 407³.
Problem 4
If a cube with a side length of 807 cm is compared to a cube with a side length of 107 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 807 cm is 525,344,343 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 807 means multiplying 807 by itself three times: 807 × 807 = 650,249, and then 650,249 × 807 = 525,344,343.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 525,344,343 cm³.
Problem 5
Estimate the cube 806.9 using the cube 807.
The cube of 806.9 is approximately 525,344,343.
Explanation
First, identify the cube of 807, The cube of 807 is 807³ = 525,344,343.
Since 806.9 is only a tiny bit less than 807, the cube of 806.9 will be almost the same as the cube of 807.
The cube of 806.9 is approximately 525,344,343 because the difference between 806.9 and 807 is very small.
So, we can approximate the value as 525,344,343.
FAQs on Cube of 807
1.What are the perfect cubes up to 807?
2.How do you calculate 807³?
3.What is the meaning of 807³?
4.What is the cube root of 807?
5.Is 807 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 807?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 807?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 807
- 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.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Cube Root: The value that, when multiplied by itself three times, gives the original number.
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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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