Last updated on June 3rd, 2025
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 378.
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 378 can be written as 378³, which is the exponential form.
Or it can also be written in arithmetic form as, 378 × 378 × 378.
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. 378³ = 378 × 378 × 378
Step 2: You get 53,787,432 as the answer. Hence, the cube of 378 is 53,787,432.
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 378 into two parts, as 300 and 78. Let a = 300 and b = 78, so a + b = 378
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 300³ 3a²b = 3 × 300² × 78 3ab² = 3 × 300 × 78² b³ = 78³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (300 + 78)³ = 300³ + 3 × 300² × 78 + 3 × 300 × 78² + 78³ 378³ = 27,000,000 + 21,060,000 + 5,461,200 + 474,232 378³ = 53,787,432
Step 5: Hence, the cube of 378 is 53,787,432.
To find the cube of 378 using a calculator, input the number 378 and use the cube function (if available) or multiply 378 × 378 × 378. This operation calculates the value of 378³, resulting in 53,787,432. 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 7 and 8
Step 3: If the calculator has a cube function, press it to calculate 378³.
Step 4: If there is no cube function on the calculator, simply multiply 378 three times manually.
Step 5: The calculator will display 53,787,432.
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 378?
The cube of 378 is 53,787,432 and the cube root of 378 is approximately 7.216.
First, let’s find the cube of 378.
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 378³ = 53,787,432
Next, we must find the cube root of 378
We know that 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√378 ≈ 7.216
Hence the cube of 378 is 53,787,432 and the cube root of 378 is approximately 7.216.
If the side length of the cube is 378 cm, what is the volume?
The volume is 53,787,432 cm³.
Use the volume formula for a cube V = Side³.
Substitute 378 for the side length: V = 378³ = 53,787,432 cm³.
How much larger is 378³ than 278³?
378³ – 278³ = 34,931,156.
First find the cube of 378³, that is 53,787,432
Next, find the cube of 278³, which is 18,856,276
Now, find the difference between them using the subtraction method. 53,787,432 – 18,856,276 = 34,931,156
Therefore, the 378³ is 34,931,156 larger than 278³.
If a cube with a side length of 378 cm is compared to a cube with a side length of 78 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 378 cm is 53,787,432 cm³
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 378 means multiplying 378 by itself three times: 378 × 378 = 142,884, and then 142,884 × 378 = 53,787,432.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 53,787,432 cm³.
Estimate the cube 377.9 using the cube 378.
The cube of 377.9 is approximately 53,787,432.
First, identify the cube of 378,
The cube of 378 is 378³ = 53,787,432.
Since 377.9 is only a tiny bit less than 378, the cube of 377.9 will be almost the same as the cube of 378.
The cube of 377.9 is approximately 53,787,432 because the difference between 377.9 and 378 is very small.
So, we can approximate the value as 53,787,432.
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.