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 the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 198.
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 multiplied by itself three times results in a negative number. The cube of 198 can be written as 198³, which is the exponential form. Or it can also be written in arithmetic form as 198 × 198 × 198.
To determine whether a number is a cube number, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help find the cube of numbers faster and easier without confusion during evaluation.
The multiplication method is a process in mathematics used to find the product of 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. 198³ = 198 × 198 × 198
Step 2: You get 7,774,872 as the answer.
Hence, the cube of 198 is 7,774,872.
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 198 into two parts.
Let a = 200 and b = -2, so a + b = 198
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ , 3a²b = 3 × 200² × (-2) , 3ab² = 3 × 200 × (-2)² , b³ = (-2)³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(200 - 2)³ = 200³ + 3 × 200² × (-2) + 3 × 200 × (-2)² + (-2)³ 198³
= 8,000,000 - 240,000 + 2,400 - 8 198³ = 7,774,872
Step 5: Hence, the cube of 198 is 7,774,872.
To find the cube of 198 using a calculator, input the number 198 and use the cube function (if available) or multiply 198 × 198 × 198. This operation calculates the value of 198³, resulting in 7,774,872. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1, followed by 9, and then 8.
Step 3: If the calculator has a cube function, press it to calculate 198³.
Step 4: If there is no cube function on the calculator, simply multiply 198 three times manually.
Step 5: The calculator will display 7,774,872.
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 198?
The cube of 198 is 7,774,872, and the cube root of 198 is approximately 5.818.
First, let’s find the cube of 198.
We know that the cube of a number x³ = y,
where x is the given number, and y is the cubed value of that number.
So, we get 198³ = 7,774,872.
Next, we must find the cube root of 198.
We know that the cube root of a number ‘x’ is 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√198 ≈ 5.818.
Hence, the cube of 198 is 7,774,872, and the cube root of 198 is approximately 5.818.
If the side length of the cube is 198 cm, what is the volume?
The volume is 7,774,872 cm³.
Use the volume formula for a cube V = side³.
Substitute 198 for the side length: V = 198³ = 7,774,872 cm³.
How much larger is 198³ than 188³?
198³ – 188³ = 2,376,872.
First, find the cube of 198³, that is 7,774,872.
Next, find the cube of 188³, which is 5,398,000.
Now, find the difference between them using the subtraction method.
7,774,872 - 5,398,000 = 2,376,872.
Therefore, 198³ is 2,376,872 larger than 188³.
If a cube with a side length of 198 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 198 cm is 7,774,872 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 198 means multiplying 198 by itself three times: 198 × 198 = 39,204, and then 39,204 × 198 = 7,774,872.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 7,774,872 cm³.
Estimate the cube of 197.9 using the cube of 198.
The cube of 197.9 is approximately 7,774,872.
First, identify the cube of 198.
The cube of 198 is 198³ = 7,774,872.
Since 197.9 is only a tiny bit less than 198, the cube of 197.9 will be almost the same as the cube of 198.
The cube of 197.9 is approximately 7,774,872 because the difference between 197.9 and 198 is very small.
So, we can approximate the value as 7,774,872.
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.