115 LearnersLast updated on May 30th, 2025
Cube of 105
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 105.
Cube of 105
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 105 can be written as 105³, which is the exponential form.
Or it can also be written in arithmetic form as 105 × 105 × 105.
How to Calculate the Value of Cube of 105
In order to check whether a number is a cube number or not, we can use the following three methods, such as 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 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. 105³ = 105 × 105 × 105
Step 2: You get 1,157,625 as the answer.
Hence, the cube of 105 is 1,157,625.
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 105 into two parts, as and . Let a = 100 and b = 5, so a + b = 105
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 5 3ab² = 3 × 100 × 5² b³ = 5³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 5)³ = 100³ + 3 × 100² × 5 + 3 × 100 × 5² + 5³ 105³ = 1,000,000 + 150,000 + 7,500 + 125 105³ = 1,157,625
Step 5: Hence, the cube of 105 is 1,157,625.
Using a Calculator
To find the cube of 105 using a calculator, input the number 105 and use the cube function (if available) or multiply 105 × 105 × 105. This operation calculates the value of 105³, resulting in 1,157,625. 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 5
Step 3: If the calculator has a cube function, press it to calculate 105³.
Step 4: If there is no cube function on the calculator, simply multiply 105 three times manually.
Step 5: The calculator will display 1,157,625.
Tips and Tricks for the Cube of 105
- 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 105
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, 105 × 105 and not 105 × 105 × 105. Always remember that 105³ = 105 × 105 × 105.
Solved Examples on Cube of 105
Problem 1
What is the cube and cube root of 105?
The cube of 105 is 1,157,625 and the cube root of 105 is approximately 4.717.
Explanation
First, let’s find the cube of 105.
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 105³ = 1,157,625 Next, we must find the cube root of 105
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 ∛105 ≈ 4.717
Hence the cube of 105 is 1,157,625 and the cube root of 105 is approximately 4.717.
Problem 2
If the side length of the cube is 105 cm, what is the volume?
The volume is 1,157,625 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 105 for the side length: V = 105³ = 1,157,625 cm³.
Problem 3
How much larger is 105³ than 95³?
105³ – 95³ = 465,125.
Explanation
First find the cube of 105, that is 1,157,625
Next, find the cube of 95, which is 692,500
Now, find the difference between them using the subtraction method. 1,157,625 – 692,500 = 465,125
Therefore, the 105³ is 465,125 larger than 95³.
Problem 4
If a cube with a side length of 105 cm is compared to a cube with a side length of 15 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 105 cm is 1,157,625 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 105 means multiplying 105 by itself three times: 105 × 105 = 11,025, and then 11,025 × 105 = 1,157,625.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,157,625 cm³.
Problem 5
Estimate the cube 104.9 using the cube 105.
The cube of 104.9 is approximately 1,157,625.
Explanation
First, identify the cube of 105, The cube of 105 is 105³ = 1,157,625.
Since 104.9 is only a tiny bit less than 105, the cube of 104.9 will be almost the same as the cube of 105.
The cube of 104.9 is approximately 1,157,625 because the difference between 104.9 and 105 is very small.
So, we can approximate the value as 1,157,625.
FAQs on Cube of 105
1.What are the perfect cubes up to 105?
2.How do you calculate 105³?
3.What is the meaning of 105³?
4.What is the cube root of 105?
5.Is 105 a perfect cube?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube of 105?
8.How do technology and digital tools in Singapore support learning Algebra and Cube of 105?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Cube of 105
- 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.
- Volume of a Cube: The volume of a cube is found by raising the side length to the third power, expressed as V = Side³.
- Perfect Cube: A number that can be expressed as the cube of an integer is called a perfect cube.
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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.
