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 the cube of 509.
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 509 can be written as 509³, which is the exponential form. Or it can also be written in arithmetic form as 509 × 509 × 509.
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 used in mathematics 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. 509³ = 509 × 509 × 509 Step 2: You get 131,442,029 as the answer. Hence, the cube of 509 is 131,442,029.
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 509 into two parts.
Let a = 500 and b = 9, so a + b = 509
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 9 , 3ab² = 3 × 500 × 9² , b³ = 9³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(500 + 9)³ = 500³ + 3 × 500² × 9 + 3 × 500 × 9² + 9³ 509³
= 125,000,000 + 6,750,000 + 121,500 + 729 509³
= 131,442,229
Step 5: Hence, the cube of 509 is 131,442,229.
To find the cube of 509 using a calculator, input the number 509 and use the cube function (if available) or multiply 509 × 509 × 509. This operation calculates the value of 509³, resulting in 131,442,029. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 5 followed by 0 and 9.
Step 3: If the calculator has a cube function, press it to calculate 509³.
Step 4: If there is no cube function on the calculator, simply multiply 509 three times manually.
Step 5: The calculator will display 131,442,029.
The cube of any even number is always even, while the cube of any odd number is always odd. The product of two or more perfect cube numbers is always a perfect cube. A perfect cube can always be expressed as the product of three identical groups of equal prime factors.
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 509?
The cube of 509 is 131,442,029 and the cube root of 509 is approximately 7.989.
First, let’s find the cube of 509.
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 509³ = 131,442,029
Next, we must find the cube root of 509
We know that the 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√509 ≈ 7.989
Hence the cube of 509 is 131,442,029 and the cube root of 509 is approximately 7.989.
If the side length of a cube is 509 cm, what is the volume?
The volume is 131,442,029 cm³.
Use the volume formula for a cube V = Side³. Substitute 509 for the side length: V = 509³ = 131,442,029 cm³.
How much larger is 509³ than 409³?
509³ – 409³ = 82,702,429.
First, find the cube of 509³, that is 131,442,029
Next, find the cube of 409³, which is 48,739,600
Now, find the difference between them using the subtraction method.
131,442,029 – 48,739,600 = 82,702,429
Therefore, 509³ is 82,702,429 larger than 409³.
If a cube with a side length of 509 cm is compared to a cube with a side length of 109 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 509 cm is 131,442,029 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 509 means multiplying 509 by itself three times: 509 × 509 = 259,081, and then 259,081 × 509 = 131,442,029.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 131,442,029 cm³.
Estimate the cube of 508.9 using the cube of 509.
The cube of 508.9 is approximately 131,442,029.
First, identify the cube of 509.
The cube of 509 is 509³ = 131,442,029.
Since 508.9 is only a tiny bit less than 509, the cube of 508.9 will be almost the same as the cube of 509.
The cube of 508.9 is approximately 131,442,029 because the difference between 508.9 and 509 is very small.
So, we can approximate the value as 131,442,029.
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.