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 useful when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 687.
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 687 can be written as 687³, which is the exponential form. Or it can also be written in arithmetic form as, 687 × 687 × 687.
To check whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These methods help in cubing numbers faster and easier without confusion or errors. -
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. 687³ = 687 × 687 × 687
Step 2: You get 324,631,023 as the answer. Hence, the cube of 687 is 324,631,023.
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 687 into two parts, as 600 and 87. Let a = 600 and b = 87, so a + b = 687
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 600³
3a²b = 3 × 600² × 87
3ab² = 3 × 600 × 87²
b³ = 87³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(600 + 87)³ = 600³ + 3 × 600² × 87 + 3 × 600 × 87² + 87³
687³ = 216,000,000 + 93,960,000 + 13,658,400 + 658,503
687³ = 324,631,023
Step 5: Hence, the cube of 687 is 324,631,023.
To find the cube of 687 using a calculator, input the number 687 and use the cube function (if available) or multiply 687 × 687 × 687. This operation calculates the value of 687³, resulting in 324,631,023. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 687 into the calculator.
Step 3: If the calculator has a cube function, press it to calculate 687³.
Step 4: If there is no cube function on the calculator, simply multiply 687 three times manually.
Step 5: The calculator will display 324,631,023.
There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:
What is the cube and cube root of 687?
The cube of 687 is 324,631,023 and the cube root of 687 is approximately 8.848.
First, let’s find the cube of 687.
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 687³ = 324,631,023.
Next, we must find the cube root of 687. 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 ∛687 ≈ 8.848.
Hence the cube of 687 is 324,631,023 and the cube root of 687 is approximately 8.848.
If the side length of the cube is 687 cm, what is the volume?
The volume is 324,631,023 cm³.
Use the volume formula for a cube V = Side³. Substitute 687 for the side length: V = 687³ = 324,631,023 cm³.
How much larger is 687³ than 600³?
687³ – 600³ = 108,631,023.
First, find the cube of 687, which is 324,631,023.
Next, find the cube of 600, which is 216,000,000.
Now, find the difference between them using the subtraction method.
324,631,023 – 216,000,000 = 108,631,023.
Therefore, 687³ is 108,631,023 larger than 600³.
If a cube with a side length of 687 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 687 cm is 324,631,023 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 687 means multiplying 687 by itself three times: 687 × 687 × 687 = 324,631,023.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 324,631,023 cm³.
Estimate the cube of 686.5 using the cube of 687.
The cube of 686.5 is approximately 324,631,023.
First, identify the cube of 687, The cube of 687 is 687³ = 324,631,023.
Since 686.5 is only a tiny bit less than 687, the cube of 686.5 will be almost the same as the cube of 687.
The cube of 686.5 is approximately 324,631,023 because the difference between 686.5 and 687 is very small.
So, we can approximate the value as 324,631,023.
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.