119 LearnersLast updated on May 29th, 2025
Cube of 87
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 87.
Cube of 87
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 87 can be written as 87³, which is the exponential form.
Or it can also be written in arithmetic form as, 87 × 87 × 87.
How to Calculate the Value of Cube of 87
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 (a3)
- 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. 87³ = 87 × 87 × 87
Step 2: You get 658,503 as the answer.
Hence, the cube of 87 is 658,503.
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 87 into two parts, as 80 and 7. Let a = 80 and b = 7, so a + b = 87
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 80³ 3a²b = 3 × 80² × 7 3ab² = 3 × 80 × 7² b³ = 7³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (80 + 7)³ = 80³ + 3 × 80² × 7 + 3 × 80 × 7² + 7³ 87³ = 512,000 + 134,400 + 11,760 + 343 87³ = 658,503
Step 5: Hence, the cube of 87 is 658,503.
Using a Calculator
To find the cube of 87 using a calculator, input the number 87 and use the cube function (if available) or multiply 87 × 87 × 87. This operation calculates the value of 87³, resulting in 658,503. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 8 followed by 7
Step 3: If the calculator has a cube function, press it to calculate 87³.
Step 4: If there is no cube function on the calculator, simply multiply 87 three times manually.
Step 5: The calculator will display 658,503.
Tips and Tricks for the Cube of 87
- 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 87
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, 87 × 87 and not 87 × 87 × 87. Always remember that 87³ = 87 × 87 × 87.
Solved Examples on Cube of 87
Problem 1
What is the cube and cube root of 87?
The cube of 87 is 658,503 and the cube root of 87 is approximately 4.431.
Explanation
First, let’s find the cube of 87.
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 87³ = 658,503 Next, we must find the cube root of 87
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√87 ≈ 4.431
Hence the cube of 87 is 658,503 and the cube root of 87 is approximately 4.431.
Problem 2
If the side length of the cube is 87 cm, what is the volume?
The volume is 658,503 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 87 for the side length: V = 87³ = 658,503 cm³.
Problem 3
How much larger is 87³ than 77³?
87³ – 77³ = 347,490.
Explanation
First find the cube of 87³, which is 658,503
Next, find the cube of 77³, which is 311,013
Now, find the difference between them using the subtraction method. 658,503 – 311,013 = 347,490
Therefore, 87³ is 347,490 larger than 77³.
Problem 4
If a cube with a side length of 87 cm is compared to a cube with a side length of 37 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 87 cm is 658,503 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 87 means multiplying 87 by itself three times: 87 × 87 = 7,569, and then 7,569 × 87 = 658,503.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 658,503 cm³.
Problem 5
Estimate the cube of 86.9 using the cube of 87.
The cube of 86.9 is approximately 658,503.
Explanation
First, identify the cube of 87,
The cube of 87 is 87³ = 658,503.
Since 86.9 is only a tiny bit less than 87, the cube of 86.9 will be almost the same as the cube of 87.
The cube of 86.9 is approximately 658,503 because the difference between 86.9 and 87 is very small.
So, we can approximate the value as 658,503.
FAQs on Cube of 87
1.What are the perfect cubes up to 87?
2.How do you calculate 87³?
3.What is the meaning of 87³?
4.What is the cube root of 87?
5.Is 87 a perfect cube?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 87?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 87?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube of 87
- Binomial Formula: 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.
- Perfect Cube: A number that can be expressed as the product of three identical numbers.
- Cube Root: A number that, when multiplied by itself three times, gives the original number.
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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.
