Last updated on June 5th, 2025
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 the cube of 768.
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 768 can be written as 768³, which is the exponential form. Or it can also be written in arithmetic form as, 768 × 768 × 768.
To determine 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.
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. 768³ = 768 × 768 × 768
Step 2: You get 452,984,832 as the answer. Hence, the cube of 768 is 452,984,832.
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 768 into two parts, such as 700 and 68. Let a = 700 and b = 68, so a + b = 768
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 700³
3a²b = 3 × 700² × 68
3ab² = 3 × 700 × 68²
b³ = 68³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(700 + 68)³ = 700³ + 3 × 700² × 68 + 3 × 700 × 68² + 68³
768³ = 343,000,000 + 100,800,000 + 32,256,000 + 314,432
768³ = 452,984,832
Step 5: Hence, the cube of 768 is 452,984,832.
To find the cube of 768 using a calculator, input the number 768 and use the cube function (if available) or multiply 768 × 768 × 768. This operation calculates the value of 768³, resulting in 452,984,832. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 7, 6, and 8
Step 3: If the calculator has a cube function, press it to calculate 768³.
Step 4: If there is no cube function on the calculator, simply multiply 768 three times manually.
Step 5: The calculator will display 452,984,832.
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:
What is the cube and cube root of 768?
The cube of 768 is 452,984,832 and the cube root of 768 is approximately 9.214.
First, let’s find the cube of 768.
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 768³ = 452,984,832.
Next, we must find the cube root of 768.
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 ∛768 ≈ 9.214.
Hence the cube of 768 is 452,984,832 and the cube root of 768 is approximately 9.214.
If the side length of a cube is 768 cm, what is the volume?
The volume is 452,984,832 cm³.
Use the volume formula for a cube V = Side³.
Substitute 768 for the side length: V = 768³ = 452,984,832 cm³.
How much larger is 768³ than 500³?
768³ – 500³ = 452,484,832.
First find the cube of 768, which is 452,984,832.
Next, find the cube of 500, which is 125,000,000.
Now, find the difference between them using the subtraction method. 452,984,832 – 125,000,000 = 327,984,832.
Therefore, 768³ is 327,984,832 larger than 500³.
If a cube with a side length of 768 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 768 cm is 452,984,832 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 768 means multiplying 768 by itself three times: 768 × 768 = 589,824, and then 589,824 × 768 = 452,984,832.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 452,984,832 cm³.
Estimate the cube of 767.9 using the cube of 768.
The cube of 767.9 is approximately 452,984,832.
First, identify the cube of 768, The cube of 768 is 768³ = 452,984,832.
Since 767.9 is only a tiny bit less than 768, the cube of 767.9 will be almost the same as the cube of 768.
The cube of 767.9 is approximately 452,984,832 because the difference between 767.9 and 768 is very small.
So, we can approximate the value as 452,984,832.
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.
: He loves to play the quiz with kids through algebra to make kids love it.