101 LearnersLast updated on June 2nd, 2025
Cube of 521
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 521.
Cube of 521
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 521 can be written as 521³, which is the exponential form. Or it can also be written in arithmetic form as, 521 × 521 × 521.
How to Calculate the Value of Cube of 521
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.
521³ = 521 × 521 × 521
Step 2: You get 141,984,641 as the answer.
Hence, the cube of 521 is 141,984,641.
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 521 into two parts, as 500 and 21.
Let a = 500 and b = 21, so a + b = 521
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 21 , 3ab² = 3 × 500 × 21² , b³ = 21³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (500 + 21)³
= 500³ + 3 × 500² × 21 + 3 × 500 × 21² + 21³ 521³
= 125,000,000 + 15,750,000 + 661,500 + 9,261 521³
= 141,984,761
Step 5: Hence, the cube of 521 is 141,984,761.
Using a Calculator
To find the cube of 521 using a calculator, input the number 521 and use the cube function (if available) or multiply 521 × 521 × 521. This operation calculates the value of 521³, resulting in 141,984,761. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 5, 2, and 1
Step 3: If the calculator has a cube function, press it to calculate 521³.
Step 4: If there is no cube function on the calculator, simply multiply 521 three times manually.
Step 5: The calculator will display 141,984,761.
Tips and Tricks for the Cube of 521
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 521
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, 521 × 521 and not 521 × 521 × 521. Always remember that 521³ = 521 × 521 × 521.
Solved Examples on Cube of 521
Problem 1
What is the cube and cube root of 521?
The cube of 521 is 141,984,761 and the cube root of 521 is approximately 8.058.
Explanation
First, let’s find the cube of 521.
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 521³ = 141,984,761
Next, we must find the cube root of 521
We know that 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 ∛521 ≈ 8.058
Hence the cube of 521 is 141,984,761 and the cube root of 521 is approximately 8.058.
Problem 2
If the side length of the cube is 521 cm, what is the volume?
The volume is 141,984,761 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 521 for the side length: V = 521³ = 141,984,761 cm³.
Problem 3
How much larger is 521³ than 500³?
521³ – 500³ = 16,984,761.
Explanation
First, find the cube of 521³, that is 141,984,761
Next, find the cube of 500³, which is 125,000,000
Now, find the difference between them using the subtraction method.
141,984,761 – 125,000,000 = 16,984,761
Therefore, the 521³ is 16,984,761 larger than 500³.
Problem 4
If a cube with a side length of 521 cm is compared to a cube with a side length of 21 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 521 cm is 141,984,761 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 521 means multiplying 521 by itself three times: 521 × 521 = 271,441, and then 271,441 × 521 = 141,984,761.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 141,984,761 cm³.
Problem 5
Estimate the cube of 520 using the cube of 521.
The cube of 520 is approximately 140,608,000.
Explanation
First, identify the cube of 521, The cube of 521 is 521³ = 141,984,761.
Since 520 is only a little less than 521, the cube of 520 will be slightly smaller than the cube of 521.
The cube of 520 is approximately 140,608,000 because the difference between 520 and 521 is very small.
So, we can approximate the value as 140,608,000.
FAQs on Cube of 521
1.What are the perfect cubes up to 521?
2.How do you calculate 521³?
3.What is the meaning of 521³?
4.What is the cube root of 521?
5.Is 521 a perfect cube?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube of 521?
8.How do technology and digital tools in Singapore support learning Algebra and Cube of 521?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Cube of 521
- 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: It is 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 can be expressed as the product of three identical integers, such as 8, 27, or 64.
- Cube Root: The cube root of a number x is a number y such that y³ = x. The cube root of a number can be approximated using a calculator.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
