113 LearnersLast updated on May 28th, 2025
Cube of 72
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 72.
Cube of 72
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 72 can be written as 72³, which is the exponential form.
Or it can also be written in arithmetic form as, 72 × 72 × 72.
How to Calculate the Value of Cube of 72
In order 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 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. 72³ = 72 × 72 × 72
Step 2: You get 373,248 as the answer.
Hence, the cube of 72 is 373,248.
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 72 into two parts, as 60 and 12. Let a = 60 and b = 12, so a + b = 72
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 60³ 3a²b = 3 × 60² × 12 3ab² = 3 × 60 × 12² b³ = 12³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (60 + 12)³ = 60³ + 3 × 60² × 12 + 3 × 60 × 12² + 12³ 72³ = 216,000 + 129,600 + 25,920 + 1,728 72³ = 373,248
Step 5: Hence, the cube of 72 is 373,248.
Using a Calculator
To find the cube of 72 using a calculator, input the number 72 and use the cube function (if available) or multiply 72 × 72 × 72. This operation calculates the value of 72³, resulting in 373,248. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 7 followed by 2
Step 3: If the calculator has a cube function, press it to calculate 72³.
Step 4: If there is no cube function on the calculator, simply multiply 72 three times manually.
Step 5: The calculator will display 373,248.
Tips and Tricks for the Cube of 72
- 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 72
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, 72 × 72 and not 72 × 72 × 72. Always remember that 72³ = 72 × 72 × 72.
Solved Examples on Cube of 72
Problem 1
What is the cube and cube root of 72?
The cube of 72 is 373,248 and the cube root of 72 is approximately 4.16.
Explanation
First, let’s find the cube of 72.
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 72³ = 373,248 Next, we must find the cube root of 72
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 ∛72 ≈ 4.16
Hence the cube of 72 is 373,248 and the cube root of 72 is approximately 4.16.
Problem 2
If the side length of the cube is 72 cm, what is the volume?
The volume is 373,248 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 72 for the side length: V = 72³ = 373,248 cm³.
Problem 3
How much larger is 72³ than 62³?
72³ – 62³ = 175,768.
Explanation
First find the cube of 72³, that is 373,248
Next, find the cube of 62³, which is 197,480
Now, find the difference between them using the subtraction method. 373,248 – 197,480 = 175,768
Therefore, 72³ is 175,768 larger than 62³.
Problem 4
If a cube with a side length of 72 cm is compared to a cube with a side length of 36 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 72 cm is 373,248 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 72 means multiplying 72 by itself three times: 72 × 72 = 5,184, and then 5,184 × 72 = 373,248.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 373,248 cm³.
Problem 5
Estimate the cube 71.9 using the cube 72.
The cube of 71.9 is approximately 373,248.
Explanation
First, identify the cube of 72,
The cube of 72 is 72³ = 373,248.
Since 71.9 is only a tiny bit less than 72, the cube of 71.9 will be almost the same as the cube of 72.
The cube of 71.9 is approximately 373,248 because the difference between 71.9 and 72 is very small.
So, we can approximate the value as 373,248.
FAQs on Cube of 72
1.What are the perfect cubes up to 72?
2.How do you calculate 72³?
3.What is the meaning of 72³?
4.What is the cube root of 72?
5.Is 72 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 72?
8.How do technology and digital tools in United States support learning Algebra and Cube of 72?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 72
- 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 cube of an integer. For example, 8 is a perfect cube because it is 2³.
- Volume of a Cube: The amount of space occupied by a cube, calculated by raising the length of a side to the third power, expressed in cubic units.
About BrightChamps in United States
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.
