100 LearnersLast updated on June 3rd, 2025
Cube of 196
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 196.
Cube of 196
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 196 can be written as 196³, which is the exponential form. Or it can also be written in arithmetic form as, 196 × 196 × 196.
How to Calculate the Value of Cube of 196
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. 196³ = 196 × 196 × 196
Step 2: You get 7,529,536 as the answer.
Hence, the cube of 196 is 7,529,536.
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 196 into two parts. Let a = 190 and b = 6, so a + b = 196.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³.
Step 3: Calculate each term. a³ = 190³ , 3a²b = 3 × 190² × 6 , 3ab² = 3 × 190 × 6² , b³ = 6³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(190 + 6)³ = 190³ + 3 × 190² × 6 + 3 × 190 × 6² + 6³ 196³
= 6,859,000 + 648,600 + 20,520 + 216
Step 5: Hence, the cube of 196 is 7,529,536.
Using a Calculator
To find the cube of 196 using a calculator, input the number 196 and use the cube function (if available) or multiply 196 × 196 × 196. This operation calculates the value of 196³, resulting in 7,529,536. 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 6.
Step 3: If the calculator has a cube function, press it to calculate 196³.
Step 4: If there is no cube function on the calculator, simply multiply 196 three times manually.
Step 5: The calculator will display 7,529,536.
Tips and Tricks for the Cube of 196
- 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 196
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, 196 × 196 and not 196 × 196 × 196.
Always remember that 196³ = 196 × 196 × 196.
Solved Examples on Cube of 196
Problem 1
What is the cube and cube root of 196?
The cube of 196 is 7,529,536 and the cube root of 196 is approximately 5.825.
Explanation
First, let’s find the cube of 196. 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 196³ = 7,529,536.
Next, we must find the cube root of 196. 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√196 ≈ 5.825.
Hence, the cube of 196 is 7,529,536 and the cube root of 196 is approximately 5.825.
Problem 2
If the side length of a cube is 196 cm, what is the volume?
The volume is 7,529,536 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 196 for the side length: V = 196³ = 7,529,536 cm³.
Problem 3
How much larger is 196³ than 190³?
196³ – 190³ = 670,536.
Explanation
First, find the cube of 196, which is 7,529,536.
ext, find the cube of 190, which is 6,859,000.
Now, find the difference between them using the subtraction method.
7,529,536 – 6,859,000 = 670,536.
Therefore, 196³ is 670,536 larger than 190³.
Problem 4
If a cube with a side length of 196 cm is compared to a cube with a side length of 6 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 196 cm is 7,529,536 cm³, which is significantly larger.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 196 means multiplying 196 by itself three times: 196 × 196 × 196 = 7,529,536.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 7,529,536 cm³.
Problem 5
Estimate the cube of 195 using the cube of 196.
The cube of 195 is approximately 7,529,536.
Explanation
First, identify the cube of 196, The cube of 196 is 196³ = 7,529,536.
Since 195 is only a tiny bit less than 196, the cube of 195 will be almost the same as the cube of 196.
The cube of 195 is approximately 7,529,536 because the difference between 195 and 196 is very small.
So, we can approximate the value as 7,529,536.
FAQs on Cube of 196
1.What are the perfect cubes up to 196?
2.How do you calculate 196³?
3.What is the meaning of 196³?
4.What is the cube root of 196?
5.Is 196 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 196?
8.How do technology and digital tools in Canada support learning Algebra and Cube of 196?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube of 196
- 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.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the side length cubed.
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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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