Last updated on May 29th, 2025
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.
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.
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.
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.
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.
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.
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:
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.
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.
If the side length of the cube is 78 cm, what is the volume?
The volume is 474,552 cm³.
Use the volume formula for a cube V = Side³.
Substitute 78 for the side length: V = 78³ = 474,552 cm³.
How much larger is 78³ than 68³?
78³ – 68³ = 301,032.
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.
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
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.
Estimate the cube of 77.9 using the cube of 78.
The cube of 77.9 is approximately 474,552.
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.
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.
: He loves to play the quiz with kids through algebra to make kids love it.