Last updated on June 2nd, 2025
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 668.
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 668 can be written as 668³, which is the exponential form. Or it can also be written in arithmetic form as, 668 × 668 × 668.
In order to check whether a number is a cube number or not, we can use the following three methods, such as the 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. 668³ = 668 × 668 × 668
Step 2: You get 298,941,632 as the answer. Hence, the cube of 668 is 298,941,632.
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 668 into two parts, as 600 and 68. Let a = 600 and b = 68, so a + b = 668
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 600³ 3a²b = 3 × 600² × 68 3ab² = 3 × 600 × 68² b³ = 68³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(600 + 68)³ = 600³ + 3 × 600² × 68 + 3 × 600 × 68² + 68³
668³ = 216,000,000 + 73,440,000 + 8,294,400 + 314,432
668³ = 298,941,632
Step 5: Hence, the cube of 668 is 298,941,632.
To find the cube of 668 using a calculator, input the number 668 and use the cube function (if available) or multiply 668 × 668 × 668. This operation calculates the value of 668³, resulting in 298,941,632. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6 followed by 6 and 8
Step 3: If the calculator has a cube function, press it to calculate 668³.
Step 4: If there is no cube function on the calculator, simply multiply 668 three times manually.
Step 5: The calculator will display 298,941,632.
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 668?
The cube of 668 is 298,941,632 and the cube root of 668 is approximately 8.757.
First, let’s find the cube of 668.
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 668³ = 298,941,632
Next, we must find the cube root of 668 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 ∛668 ≈ 8.757
Hence, the cube of 668 is 298,941,632 and the cube root of 668 is approximately 8.757.
If the side length of the cube is 668 cm, what is the volume?
The volume is 298,941,632 cm³.
Use the volume formula for a cube V = Side³.
Substitute 668 for the side length: V = 668³ = 298,941,632 cm³.
How much larger is 668³ than 600³?
668³ – 600³ = 82,941,632.
First find the cube of 668³, which is 298,941,632
Next, find the cube of 600³, which is 216,000,000
Now, find the difference between them using the subtraction method.
298,941,632 – 216,000,000 = 82,941,632
Therefore, 668³ is 82,941,632 larger than 600³.
If a cube with a side length of 668 cm is compared to a cube with a side length of 68 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 668 cm is 298,941,632 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 668 means multiplying 668 by itself three times: 668 × 668 = 446,224, and then 446,224 × 668 = 298,941,632.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 298,941,632 cm³.
Estimate the cube of 668.1 using the cube of 668.
The cube of 668.1 is approximately 298,941,632.
First, identify the cube of 668, The cube of 668 is 668³ = 298,941,632.
Since 668.1 is only a tiny bit more than 668, the cube of 668.1 will be almost the same as the cube of 668.
The cube of 668.1 is approximately 298,941,632 because the difference between 668.1 and 668 is very small.
So, we can approximate the value as 298,941,632.
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.