100 LearnersLast updated on June 1st, 2025
Cube of 387
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 cubes of 387.
Cube of 387
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 387 can be written as 387³, which is the exponential form.
Or it can also be written in arithmetic form as, 387 × 387 × 387.
How to Calculate the Value of Cube of 387
In order to check whether a number is a cube number or not, we can use the following three methods: 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. 387³ = 387 × 387 × 387
Step 2: You get 57,942,003 as the answer. Hence, the cube of 387 is 57,942,003.
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 387 into two parts, as 380 and 7. Let a = 380 and b = 7, so a + b = 387
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 380³ 3a²b = 3 × 380² × 7 3ab² = 3 × 380 × 7² b³ = 7³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (380 + 7)³ = 380³ + 3 × 380² × 7 + 3 × 380 × 7² + 7³ 387³ = 54,872,000 + 302,280 + 55,860 + 343 387³ = 57,942,003
Step 5: Hence, the cube of 387 is 57,942,003.
Using a Calculator
To find the cube of 387 using a calculator, input the number 387 and use the cube function (if available) or multiply 387 × 387 × 387. This operation calculates the value of 387³, resulting in 57,942,003. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 3 followed by 8 and then 7
Step 3: If the calculator has a cube function, press it to calculate 387³.
Step 4: If there is no cube function on the calculator, simply multiply 387 three times manually.
Step 5: The calculator will display 57,942,003.
Tips and Tricks for the Cube of 387
- 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 387
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, 387 × 387 and not 387 × 387 × 387. Always remember that 387³ = 387 × 387 × 387.
Solved Examples on Cube of 387
Problem 1
What is the cube and cube root of 387?
The cube of 387 is 57,942,003 and the cube root of 387 is approximately 7.271.
Explanation
First, let’s find the cube of 387.
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 387³ = 57,942,003
Next, we must find the cube root of 387
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√387 ≈ 7.271
Hence the cube of 387 is 57,942,003 and the cube root of 387 is approximately 7.271.
Problem 2
If the side length of the cube is 387 cm, what is the volume?
The volume is 57,942,003 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 387 for the side length: V = 387³ = 57,942,003 cm³.
Problem 3
How much larger is 387³ than 380³?
387³ – 380³ = 2,826,243.
Explanation
First, find the cube of 387³, that is 57,942,003
Next, find the cube of 380³, which is 55,115,760
Now, find the difference between them using the subtraction method. 57,942,003 – 55,115,760 = 2,826,243
Therefore, 387³ is 2,826,243 larger than 380³.
Problem 4
If a cube with a side length of 387 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 387 cm is 57,942,003 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 387 means multiplying 387 by itself three times: 387 × 387 = 149,769, and then 149,769 × 387 = 57,942,003.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 57,942,003 cm³.
Problem 5
Estimate the cube of 386.9 using the cube of 387.
The cube of 386.9 is approximately 57,942,003.
Explanation
First, identify the cube of 387,
The cube of 387 is 387³ = 57,942,003.
Since 386.9 is only a tiny bit less than 387, the cube of 386.9 will be almost the same as the cube of 387.
The cube of 386.9 is approximately 57,942,003 because the difference between 386.9 and 387 is very small.
So, we can approximate the value as 57,942,003.
FAQs on Cube of 387
1.What are the perfect cubes up to 387?
2.How do you calculate 387³?
3.What is the meaning of 387³?
4.What is the cube root of 387?
5.Is 387 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 387?
8.How do technology and digital tools in United States support learning Algebra and Cube of 387?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 387
- 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 is a perfect cube if it can be expressed as the cube of an integer.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
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Jaskaran Singh Saluja
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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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