118 LearnersLast updated on May 30th, 2025
Cube of 101
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 101.
Cube of 101
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 101 can be written as 101³, which is the exponential form.
Or it can also be written in arithmetic form as, 101 × 101 × 101.
How to Calculate the Value of Cube of 101
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 you cube 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 by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number. 101³ = 101 × 101 × 101
Step 2: You get 1,030,301 as the answer.
Hence, the cube of 101 is 1,030,301.
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 101 into two parts, as 100 and 1. Let a = 100 and b = 1, so a + b = 101
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 1 3ab² = 3 × 100 × 1² b³ = 1³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 1)³ = 100³ + 3 × 100² × 1 + 3 × 100 × 1² + 1³ 101³ = 1,000,000 + 30,000 + 300 + 1 101³ = 1,030,301
Step 5: Hence, the cube of 101 is 1,030,301.
Using a Calculator
To find the cube of 101 using a calculator, input the number 101 and use the cube function (if available) or multiply 101 × 101 × 101. This operation calculates the value of 101³, resulting in 1,030,301. 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 1
Step 3: If the calculator has a cube function, press it to calculate 101³.
Step 4: If there is no cube function on the calculator, simply multiply 101 three times manually.
Step 5: The calculator will display 1,030,301.
Tips and Tricks for the Cube of 101
- 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 101
There are some typical errors that might be made during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice. That is, 101 × 101 and not 101 × 101 × 101. Always remember that 101³ = 101 × 101 × 101.
Solved Examples on Cube of 101
Problem 1
What is the cube and cube root of 101?
The cube of 101 is 1,030,301 and the cube root of 101 is approximately 4.6416.
Explanation
First, let’s find the cube of 101.
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 101³ = 1,030,301. Next, we must find the cube root of 101.
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√101 ≈ 4.6416.
Hence, the cube of 101 is 1,030,301 and the cube root of 101 is approximately 4.6416.
Problem 2
If the side length of the cube is 101 cm, what is the volume?
The volume is 1,030,301 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 101 for the side length: V = 101³ = 1,030,301 cm³.
Problem 3
How much larger is 101³ than 100³?
101³ – 100³ = 30,301.
Explanation
First, find the cube of 101, which is 1,030,301.
Next, find the cube of 100, which is 1,000,000.
Now, find the difference between them using the subtraction method. 1,030,301 – 1,000,000 = 30,301.
Therefore, 101³ is 30,301 larger than 100³.
Problem 4
If a cube with a side length of 101 cm is compared to a cube with a side length of 50 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 101 cm is 1,030,301 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 101 means multiplying 101 by itself three times: 101 × 101 = 10,201, and then 10,201 × 101 = 1,030,301.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,030,301 cm³.
Problem 5
Estimate the cube of 100.1 using the cube of 101.
The cube of 100.1 is approximately 1,030,301.
Explanation
First, identify the cube of 101,
The cube of 101 is 101³ = 1,030,301.
Since 100.1 is only slightly less than 101, the cube of 100.1 will be almost the same as the cube of 101.
The cube of 100.1 is approximately 1,030,301 because the difference between 100.1 and 101 is very small.
So, we can approximate the value as 1,030,301.
FAQs on Cube of 101
1.What are the perfect cubes up to 101?
2.How do you calculate 101³?
3.What is the meaning of 101³?
4.What is the cube root of 101?
5.Is 101 a perfect cube?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Cube of 101?
8.How do technology and digital tools in Qatar support learning Algebra and Cube of 101?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Cube of 101
- 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.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
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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
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