118 LearnersLast updated on May 30th, 2025
Cube of 106
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 the cube of 106.
Cube of 106
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 106 can be written as 106³, which is the exponential form.
Or it can also be written in arithmetic form as 106 × 106 × 106.
How to Calculate the Value of Cube of 106
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 (a3)
- Using a Calculator
By Multiplication Method
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. 106³ = 106 × 106 × 106
Step 2: You get 1,191,016 as the answer.
Hence, the cube of 106 is 1,191,016.
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 106 into two parts. Let a = 100 and b = 6, so a + b = 106
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 6 3ab² = 3 × 100 × 6² b³ = 6³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 6)³ = 100³ + 3 × 100² × 6 + 3 × 100 × 6² + 6³ 106³ = 1,000,000 + 180,000 + 10,800 + 216 106³ = 1,191,016
Step 5: Hence, the cube of 106 is 1,191,016.
Using a Calculator
To find the cube of 106 using a calculator, input the number 106 and use the cube function (if available) or multiply 106 × 106 × 106. This operation calculates the value of 106³, resulting in 1,191,016. 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 0 and 6
Step 3: If the calculator has a cube function, press it to calculate 106³.
Step 4: If there is no cube function on the calculator, simply multiply 106 three times manually.
Step 5: The calculator will display 1,191,016.
Tips and Tricks for the Cube of 106
- 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 106
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, 106 × 106 and not 106 × 106 × 106. Always remember that 106³ = 106 × 106 × 106.
Solved Examples on Cube of 106
Problem 1
What is the cube and cube root of 106?
The cube of 106 is 1,191,016, and the cube root of 106 is approximately 4.726.
Explanation
First, let’s find the cube of 106.
We know that the 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 106³ = 1,191,016 Next, we must find the cube root of 106
We know that the 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√106 ≈ 4.726
Hence, the cube of 106 is 1,191,016, and the cube root of 106 is approximately 4.726.
Problem 2
If the side length of a cube is 106 cm, what is the volume?
The volume is 1,191,016 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 106 for the side length: V = 106³ = 1,191,016 cm³.
Problem 3
How much larger is 106³ than 100³?
106³ – 100³ = 191,016.
Explanation
First, find the cube of 106³, which is 1,191,016.
Next, find the cube of 100³, which is 1,000,000.
Now, find the difference between them using the subtraction method. 1,191,016 – 1,000,000 = 191,016
Therefore, 106³ is 191,016 larger than 100³.
Problem 4
If a cube with a side length of 106 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 106 cm is 1,191,016 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 106 means multiplying 106 by itself three times: 106 × 106 = 11,236, and then 11,236 × 106 = 1,191,016.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,191,016 cm³.
Problem 5
Estimate the cube of 105.9 using the cube of 106.
The cube of 105.9 is approximately 1,191,016.
Explanation
First, identify the cube of 106.
The cube of 106 is 106³ = 1,191,016.
Since 105.9 is only a tiny bit less than 106, the cube of 105.9 will be almost the same as the cube of 106.
The cube of 105.9 is approximately 1,191,016 because the difference between 105.9 and 106 is very small.
So, we can approximate the value as 1,191,016.
FAQs on Cube of 106
1.What are the perfect cubes up to 106?
2.How do you calculate 106³?
3.What is the meaning of 106³?
4.What is the cube root of 106?
5.Is 106 a perfect cube?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube of 106?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube of 106?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube of 106
- 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, which equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Volume of a Cube: The amount of space enclosed within a cube, calculated as the cube of the side length (Side³).
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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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