102 LearnersLast updated on June 3rd, 2025
Cube of 197
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 the cube of 197.
Cube of 197
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 197 can be written as 197³, which is the exponential form. Or it can also be written in arithmetic form as 197 × 197 × 197.
How to Calculate the Value of Cube of 197
In order to check whether a number is a cube number or not, we can use the following three methods: 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
- 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.
197³ = 197 × 197 × 197
Step 2: Calculate the product to get the answer. Hence, the cube of 197 is 7,655,813.
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 197 into two parts.
Let a = 190 and b = 7, so a + b = 197
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 190³ , 3a²b = 3 × 190² × 7 , 3ab² = 3 × 190 × 7² , b³ = 7³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(190 + 7)³ = 190³ + 3 × 190² × 7 + 3 × 190 × 7² + 7³ 197³
= 6,859,000 + 794,430 + 27,930 + 343 197³
= 7,655,813
Step 5: Hence, the cube of 197 is 7,655,813.
Using a Calculator
To find the cube of 197 using a calculator, input the number 197 and use the cube function (if available) or multiply 197 × 197 × 197. This operation calculates the value of 197³, resulting in 7,655,813. 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, then 7.
Step 3: If the calculator has a cube function, press it to calculate 197³.
Step 4: If there is no cube function on the calculator, simply multiply 197 three times manually.
Step 5: The calculator will display 7,655,813.
Tips and Tricks for the Cube of 197
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 197
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, 197 × 197 and not 197 × 197 × 197. Always remember that 197³ = 197 × 197 × 197.
Solved Examples on Cube of 197
Problem 1
What is the cube and cube root of 197?
The cube of 197 is 7,655,813 and the cube root of 197 is approximately 5.82.
Explanation
First, let’s find the cube of 197.
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 197³ = 7,655,813
Next, we must find the cube root of 197.
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 ∛197 ≈ 5.82
Hence the cube of 197 is 7,655,813 and the cube root of 197 is approximately 5.82.
Problem 2
If the side length of the cube is 197 cm, what is the volume?
The volume is 7,655,813 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 197 for the side length: V = 197³ = 7,655,813 cm³.
Problem 3
How much larger is 197³ than 190³?
197³ - 190³ = 796,813.
Explanation
First find the cube of 197³, that is 7,655,813.
Next, find the cube of 190³, which is 6,859,000.
Now, find the difference between them using the subtraction method.
7,655,813 - 6,859,000 = 796,813
Therefore, 197³ is 796,813 larger than 190³.
Problem 4
If a cube with a side length of 197 cm is compared to a cube with a side length of 7 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 197 cm is 7,655,813 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 197 means multiplying 197 by itself three times: 197 × 197 = 38,809, and then 38,809 × 197 = 7,655,813.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 7,655,813 cm³.
Problem 5
Estimate the cube of 196.9 using the cube of 197.
The cube of 196.9 is approximately 7,655,813.
Explanation
First, identify the cube of 197.
The cube of 197 is 197³ = 7,655,813.
Since 196.9 is only a tiny bit less than 197, the cube of 196.9 will be almost the same as the cube of 197.
The cube of 196.9 is approximately 7,655,813 because the difference between 196.9 and 197 is very small.
So, we can approximate the value as 7,655,813.
FAQs on Cube of 197
1.What are the perfect cubes up to 197?
2.How do you calculate 197³?
3.What is the meaning of 197³?
4.What is the cube root of 197?
5.Is 197 a perfect cube?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of 197?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 197?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube of 197
- 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 to 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Volume: The amount of space inside a 3-dimensional object, calculated as a cube's 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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
