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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 653.
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 653 can be written as 653³, which is the exponential form. Or it can also be written in arithmetic form as 653 × 653 × 653.
In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help to cube 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. 653³ = 653 × 653 × 653
Step 2: You get 278,464,177 as the answer. Hence, the cube of 653 is 278,464,177.
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 653 into two parts. Let a = 650 and b = 3, so a + b = 653
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 650³
3a²b = 3 × 650² × 3
3ab² = 3 × 650 × 3²
b³ = 3³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(650 + 3)³ = 650³ + 3 × 650² × 3 + 3 × 650 × 3² + 3³
653³ = 274,625,000 + 38,025 + 5,850 + 27
653³ = 278,464,177
Step 5: Hence, the cube of 653 is 278,464,177.
To find the cube of 653 using a calculator, input the number 653 and use the cube function (if available) or multiply 653 × 653 × 653. This operation calculates the value of 653³, resulting in 278,464,177. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6, 5, and 3.
Step 3: If the calculator has a cube function, press it to calculate 653³.
Step 4: If there is no cube function on the calculator, simply multiply 653 three times manually.
Step 5: The calculator will display 278,464,177.
There are some typical errors that might be made 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 653?
The cube of 653 is 278,464,177, and the cube root of 653 is approximately 8.671.
First, let’s find the cube of 653.
We know that the cube of a number is expressed as x³ = y Where x is the given number, and y is the cubed value of that number.
So, we get 653³ = 278,464,177.
Next, we must find the cube root of 653.
We know that the cube root of a number x is expressed as ∛x = y Where x is the given number, and y is the cube root value of the number.
So, we get ∛653 ≈ 8.671.
Hence, the cube of 653 is 278,464,177, and the cube root of 653 is approximately 8.671.
If the side length of the cube is 653 cm, what is the volume?
The volume is 278,464,177 cm³.
Use the volume formula for a cube V = Side³.
Substitute 653 for the side length: V = 653³ = 278,464,177 cm³.
How much larger is 653³ than 403³?
653³ – 403³ = 214,464,177.
First, find the cube of 653, which is 278,464,177.
Next, find the cube of 403, which is 64,000.
Now, find the difference between them using the subtraction method: 278,464,177 – 64,000 = 214,464,177.
Therefore, 653³ is 214,464,177 larger than 403³.
If a cube with a side length of 653 cm is compared to a cube with a side length of 13 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 653 cm is 278,464,177 cm³.
To find its volume, multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 653 means multiplying 653 by itself three times: 653 × 653 = 426,409, and then 426,409 × 653 = 278,464,177.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 278,464,177 cm³.
Estimate the cube of 652.9 using the cube of 653.
The cube of 652.9 is approximately 278,464,177.
First, identify the cube of 653, The cube of 653 is 653³ = 278,464,177.
Since 652.9 is only a tiny bit less than 653, the cube of 652.9 will be almost the same as the cube of 653.
The cube of 652.9 is approximately 278,464,177 because the difference between 652.9 and 653 is very small.
So, we can approximate the value as 278,464,177.
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.