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 680.
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 680 can be written as 680³, which is the exponential form. Or it can also be written in arithmetic form as, 680 × 680 × 680.
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.
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. 680³ = 680 × 680 × 680
Step 2: You get 314,432,000 as the answer. Hence, the cube of 680 is 314,432,000.
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 680 into two parts, such as 600 and 80. Let a = 600 and b = 80, so a + b = 680
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 600³
3a²b = 3 × 600² × 80
3ab² = 3 × 600 × 80²
b³ = 80³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(600 + 80)³ = 600³ + 3 × 600² × 80 + 3 × 600 × 80² + 80³
680³ = 216,000,000 + 86,400,000 + 23,040,000 + 512,000
680³ = 314,432,000
Step 5: Hence, the cube of 680 is 314,432,000.
To find the cube of 680 using a calculator, input the number 680 and use the cube function (if available) or multiply 680 × 680 × 680. This operation calculates the value of 680³, resulting in 314,432,000. 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 8 and 0
Step 3: If the calculator has a cube function, press it to calculate 680³.
Step 4: If there is no cube function on the calculator, simply multiply 680 three times manually.
Step 5: The calculator will display 314,432,000.
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 680?
The cube of 680 is 314,432,000 and the cube root of 680 is approximately 8.79.
First, let’s find the cube of 680.
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 680³ = 314,432,000
Next, we must find the cube root of 680 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 ∛680 ≈ 8.79
Hence the cube of 680 is 314,432,000 and the cube root of 680 is approximately 8.79.
If the side length of the cube is 680 cm, what is the volume?
The volume is 314,432,000 cm³.
Use the volume formula for a cube V = Side³.
Substitute 680 for the side length: V = 680³ = 314,432,000 cm³.
How much larger is 680³ than 600³?
680³ – 600³ = 98,432,000.
First find the cube of 680³, that is 314,432,000
Next, find the cube of 600³, which is 216,000,000
Now, find the difference between them using the subtraction method. 314,432,000 – 216,000,000 = 98,432,000
Therefore, the 680³ is 98,432,000 larger than 600³.
If a cube with a side length of 680 cm is compared to a cube with a side length of 80 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 680 cm is 314,432,000 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 680 means multiplying 680 by itself three times: 680 × 680 = 462,400, and then 462,400 × 680 = 314,432,000.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 314,432,000 cm³.
Estimate the cube 679.9 using the cube 680.
The cube of 679.9 is approximately 314,432,000.
First, identify the cube of 680, The cube of 680 is 680³ = 314,432,000.
Since 679.9 is only a tiny bit less than 680, the cube of 679.9 will be almost the same as the cube of 680.
The cube of 679.9 is approximately 314,432,000 because the difference between 679.9 and 680 is very small.
So, we can approximate the value as 314,432,000.
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.