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 513.
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 513 can be written as 513³, which is the exponential form. Or it can also be written in arithmetic form as, 513 × 513 × 513.
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 students cube numbers faster and more easily without feeling confused or stuck while evaluating the answers.
The multiplication method is a process in mathematics used to find the product of 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.
513³ = 513 × 513 × 513
Step 2: You get 135,796,257 as the answer.
Hence, the cube of 513 is 135,796,257.
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 513 into two parts.
Let a = 500 and b = 13, so a + b = 513
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 13 , 3ab² = 3 × 500 × 13² , b³ = 13³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(500 + 13)³ = 500³ + 3 × 500² × 13 + 3 × 500 × 13² + 13³
513³ = 125,000,000 + 97,500 + 101,400 + 2,197
513³ = 135,796,097
Step 5: Hence, the cube of 513 is 135,796,257.
To find the cube of 513 using a calculator, input the number 513 and use the cube function (if available) or multiply 513 × 513 × 513. This operation calculates the value of 513³, resulting in 135,796,257. 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 1 and 3.
Step 3: If the calculator has a cube function, press it to calculate 513³.
Step 4: If there is no cube function on the calculator, simply multiply 513 three times manually.
Step 5: The calculator will display 135,796,257.
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 students might make 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 513?
The cube of 513 is 135,796,257 and the cube root of 513 is approximately 8.051.
First, let’s find the cube of 513.
We know that the cube of a number is such that x³ = y.
Where x is the given number, and y is the cubed value of that number.
So, we get 513³ = 135,796,257.
Next, we must find the cube root of 513.
We know that the cube root of a number ‘x’ is 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√513 ≈ 8.051.
Hence the cube of 513 is 135,796,257 and the cube root of 513 is approximately 8.051.
If the side length of a cube is 513 cm, what is the volume?
The volume is 135,796,257 cm³.
Use the volume formula for a cube V = Side³.
Substitute 513 for the side length: V = 513³ = 135,796,257 cm³.
How much larger is 513³ than 413³?
513³ – 413³ = 88,515,793.
First find the cube of 513, that is 135,796,257.
Next, find the cube of 413, which is 47,280,464.
Now, find the difference between them using the subtraction method.
135,796,257 – 47,280,464 = 88,515,793.
Therefore, 513³ is 88,515,793 larger than 413³.
If a cube with a side length of 513 cm is compared to a cube with a side length of 113 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 513 cm is 135,796,257 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 513 means multiplying 513 by itself three times.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 135,796,257 cm³.
Estimate the cube of 512.9 using the cube of 513.
The cube of 512.9 is approximately 135,796,257.
First, identify the cube of 513.
The cube of 513 is 513³ = 135,796,257.
Since 512.9 is only a tiny bit less than 513, the cube of 512.9 will be almost the same as the cube of 513.
The cube of 512.9 is approximately 135,796,257 because the difference between 512.9 and 513 is very small.
So, we can approximate the value as 135,796,257.
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.