101 LearnersLast updated on June 2nd, 2025
Cube of 516
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 516.
Cube of 516
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 516 can be written as 516³, which is the exponential form. Or it can also be written in arithmetic form as, 516 × 516 × 516.
How to Calculate the Value of Cube of 516
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.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By Multiplication Method
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.
516³ = 516 × 516 × 516
Step 2: You get 137,256,096 as the answer.
Hence, the cube of 516 is 137,256,096.
Using a Formula (a³)
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 516 into two parts, as 500 and 16.
Let a = 500 and b = 16, so a + b = 516
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 16 , 3ab² = 3 × 500 × 16² , b³ = 16³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(500 + 16)³ = 500³ + 3 × 500² × 16 + 3 × 500 × 16² + 16³
516³ = 125,000,000 + 12,000,000 + 384,000 + 4,096 516³
= 137,256,096
Step 5: Hence, the cube of 516 is 137,256,096.
Using a Calculator
To find the cube of 516 using a calculator, input the number 516 and use the cube function (if available) or multiply 516 × 516 × 516. This operation calculates the value of 516³, resulting in 137,256,096. 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 6
Step 3: If the calculator has a cube function, press it to calculate 516³.
Step 4: If there is no cube function on the calculator, simply multiply 516 three times manually.
Step 5: The calculator will display 137,256,096.
Tips and Tricks for the Cube of 516
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.
Common Mistakes to Avoid When Calculating the Cube of 516
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:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 516 × 516 and not 516 × 516 × 516. Always remember that 516³ = 516 × 516 × 516.
Solved Examples on Cube of 516
Problem 1
What is the cube and cube root of 516?
The cube of 516 is 137,256,096 and the cube root of 516 is approximately 8.0507.
Explanation
First, let’s find the cube of 516.
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 516³ = 137,256,096
Next, we must find the cube root of 516
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√516 ≈ 8.0507
Hence the cube of 516 is 137,256,096 and the cube root of 516 is approximately 8.0507.
Problem 2
If the side length of the cube is 516 cm, what is the volume?
The volume is 137,256,096 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 516 for the side length: V = 516³ = 137,256,096 cm³.
Problem 3
How much larger is 516³ than 500³?
516³ – 500³ = 12,256,096.
Explanation
First find the cube of 516, that is 137,256,096
Next, find the cube of 500, which is 125,000,000
Now, find the difference between them using the subtraction method.
137,256,096 – 125,000,000 = 12,256,096
Therefore, the 516³ is 12,256,096 larger than 500³.
Problem 4
If a cube with a side length of 516 cm is compared to a cube with a side length of 16 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 516 cm is 137,256,096 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 516 means multiplying 516 by itself three times: 516 × 516 = 266,256, and then 266,256 × 516 = 137,256,096.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 137,256,096 cm³.
Problem 5
Estimate the cube of 515.5 using the cube of 516.
The cube of 515.5 is approximately 137,256,096.
Explanation
First, identify the cube of 516.
The cube of 516 is 516³ = 137,256,096.
Since 515.5 is very close to 516, the cube of 515.5 will be almost the same as the cube of 516.
The cube of 515.5 is approximately 137,256,096 because the difference between 515.5 and 516 is very small.
So, we can approximate the value as 137,256,096.
FAQs on Cube of 516
1.What are the perfect cubes up to 516?
2.How do you calculate 516³?
3.What is the meaning of 516³?
4.What is the cube root of 516?
5.Is 516 a perfect cube?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Cube of 516?
8.How do technology and digital tools in India support learning Algebra and Cube of 516?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Cube of 516
- Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
- Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
- Exponential Form: A way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.
- Perfect Cube: A number that is the cube of an integer.
- Volume: The amount of space occupied by a 3-dimensional object, measured in cubic units.
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Jaskaran Singh Saluja
About the Author
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.
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