Last updated on June 3rd, 2025
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used in while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 689.
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 689 can be written as 689³, which is the exponential form. Or it can also be written in arithmetic form as, 689 × 689 × 689.
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. 689³ = 689 × 689 × 689
Step 2: You get 326,651,969 as the answer. Hence, the cube of 689 is 326,651,969.
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 689 into two parts, as and . Let a = 680 and b = 9, so a + b = 689
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³= 680³
3a²b = 3 × 680² × 9
3ab² = 3 × 680 × 9²
b³ = 9³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(680 + 9)³ = 680³ + 3 × 680² × 9 + 3 × 680 × 9² + 9³
689³ = 314,432,000 + 124,272 + 16,632 + 729
689³ = 326,651,969
Step 5: Hence, the cube of 689 is 326,651,969.
To find the cube of 689 using a calculator, input the number 689 and use the cube function (if available) or multiply 689 × 689 × 689. This operation calculates the value of 689³, resulting in 326,651,969. 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 then 9
Step 3: If the calculator has a cube function, press it to calculate 689³.
Step 4: If there is no cube function on the calculator, simply multiply 689 three times manually.
Step 5: The calculator will display 326,651,969.
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 689?
The cube of 689 is 326,651,969 and the cube root of 689 is approximately 8.878.
First, let’s find the cube of 689.
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 689³ = 326,651,969
Next, we must find the cube root of 689 We know that 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√689 ≈ 8.878
Hence, the cube of 689 is 326,651,969 and the cube root of 689 is approximately 8.878.
If the side length of the cube is 689 cm, what is the volume?
The volume is 326,651,969 cm³.
Use the volume formula for a cube V = Side³.
Substitute 689 for the side length: V = 689³ = 326,651,969 cm³.
How much larger is 689³ than 680³?
689³ – 680³ = 7,573,969.
First find the cube of 689, that is 326,651,969
Next, find the cube of 680, which is 314,432,000
Now, find the difference between them using the subtraction method. 326,651,969 – 314,432,000 = 7,573,969
Therefore, the 689³ is 7,573,969 larger than 680³.
If a cube with a side length of 689 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 689 cm is 326,651,969 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 689 means multiplying 689 by itself three times: 689 × 689 = 474,721, and then 474,721 × 689 = 326,651,969.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 326,651,969 cm³.
Estimate the cube 688.9 using the cube 689.
The cube of 688.9 is approximately 326,651,969.
First, identify the cube of 689, The cube of 689 is 689³ = 326,651,969.
Since 688.9 is only a tiny bit less than 689, the cube of 688.9 will be almost the same as the cube of 689.
The cube of 688.9 is approximately 326,651,969 because the difference between 688.9 and 689 is very small.
So, we can approximate the value as 326,651,969.
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.