117 LearnersLast updated on May 29th, 2025
Cube of 78
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 cubes of 78.
Cube of 78
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, because a negative number by itself three times results in a negative number.
The cube of 78 can be written as 78³, which is the exponential form.
Or it can also be written in arithmetic form as, 78 × 78 × 78.
How to Calculate the Value of Cube of 78
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. 78³ = 78 × 78 × 78
Step 2: You get 474,552 as the answer.
Hence, the cube of 78 is 474,552.
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 78 into two parts, as 70 and 8. Let a = 70 and b = 8, so a + b = 78
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 70³ 3a²b = 3 × 70² × 8 3ab² = 3 × 70 × 8² b³ = 8³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (70 + 8)³ = 70³ + 3 × 70² × 8 + 3 × 70 × 8² + 8³ 78³ = 343,000 + 117,600 + 13,440 + 512 78³ = 474,552
Step 5: Hence, the cube of 78 is 474,552.
Using a Calculator
To find the cube of 78 using a calculator, input the number 78 and use the cube function (if available) or multiply 78 × 78 × 78. This operation calculates the value of 78³, resulting in 474,552. 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 8
Step 3: If the calculator has a cube function, press it to calculate 78³.
Step 4: If there is no cube function on the calculator, simply multiply 78 three times manually.
Step 5: The calculator will display 474,552.
Tips and Tricks for the Cube of 78
- 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 78
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, 78 × 78 and not 78 × 78 × 78. Always remember that 78³ = 78 × 78 × 78.
Solved Examples on Cube of 78
Problem 1
What is the cube and cube root of 78?
The cube of 78 is 474,552 and the cube root of 78 is approximately 4.284.
Explanation
First, let’s find the cube of 78.
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 78³ = 474,552 Next, we must find the cube root of 78
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 ∛78 ≈ 4.284
Hence the cube of 78 is 474,552 and the cube root of 78 is approximately 4.284.
Problem 2
If the side length of the cube is 78 cm, what is the volume?
The volume is 474,552 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 78 for the side length: V = 78³ = 474,552 cm³.
Problem 3
How much larger is 78³ than 68³?
78³ – 68³ = 301,032.
Explanation
First find the cube of 78³, that is 474,552
Next, find the cube of 68³, which is 173,520
Now, find the difference between them using the subtraction method. 474,552 – 173,520 = 301,032
Therefore, 78³ is 301,032 larger than 68³.
Problem 4
If a cube with a side length of 78 cm is compared to a cube with a side length of 18 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 78 cm is 474,552 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 78 means multiplying 78 by itself three times: 78 × 78 = 6,084, and 6,084 × 78 = 474,552.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 474,552 cm³.
Problem 5
Estimate the cube of 77.9 using the cube of 78.
The cube of 77.9 is approximately 474,552.
Explanation
First, identify the cube of 78,
The cube of 78 is 78³ = 474,552.
Since 77.9 is only a tiny bit less than 78, the cube of 77.9 will be almost the same as the cube of 78.
The cube of 77.9 is approximately 474,552 because the difference between 77.9 and 78 is very small.
So, we can approximate the value as 474,552.
FAQs on Cube of 78
1.What are the perfect cubes up to 78?
2.How do you calculate 78³?
3.What is the meaning of 78³?
4.What is the cube root of 78?
5.Is 78 a perfect cube?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Cube of 78?
8.How do technology and digital tools in Canada support learning Algebra and Cube of 78?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube of 78
- 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.
- Cube Root: The cube root of a number is what number multiplied by itself three times equals the original number.
- Volume of a Cube: It is the space inside a cube, calculated as the side length raised to the power of three.
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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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