116 LearnersLast updated on May 28th, 2025
Cube of 69
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 cubes of 69.
Cube of 69
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 69 can be written as 69³, which is the exponential form.
Or it can also be written in arithmetic form as, 69 × 69 × 69.
How to Calculate the Value of Cube of 69
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 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. 69³ = 69 × 69 × 69
Step 2: You get 328,509 as the answer.
Hence, the cube of 69 is 328,509.
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 69 into two parts, as 60 and 9. Let a = 60 and b = 9, so a + b = 69
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 60³ 3a²b = 3 × 60² × 9 3ab² = 3 × 60 × 9² b³ = 9³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (60 + 9)³ = 60³ + 3 × 60² × 9 + 3 × 60 × 9² + 9³ 69³ = 216,000 + 97,200 + 14,580 + 729 69³ = 328,509
Step 5: Hence, the cube of 69 is 328,509.
Using a Calculator
To find the cube of 69 using a calculator, input the number 69 and use the cube function (if available) or multiply 69 × 69 × 69. This operation calculates the value of 69³, resulting in 328,509. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6 followed by 9
Step 3: If the calculator has a cube function, press it to calculate 69³.
Step 4: If there is no cube function on the calculator, simply multiply 69 three times manually.
Step 5: The calculator will display 328,509.
Tips and Tricks for the Cube of 69
- 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 69
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, 69 × 69 and not 69 × 69 × 69. Always remember that 69³ = 69 × 69 × 69.
Solved Examples on Cube of 69
Problem 1
What is the cube and cube root of 69?
The cube of 69 is 328,509 and the cube root of 69 is approximately 4.101.
Explanation
First, let’s find the cube of 69.
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 69³ = 328,509 Next, we must find the cube root of 69
We know that the 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 ∛69 ≈ 4.101
Hence the cube of 69 is 328,509 and the cube root of 69 is approximately 4.101.
Problem 2
If the side length of the cube is 69 cm, what is the volume?
The volume is 328,509 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 69 for the side length: V = 69³ = 328,509 cm³.
Problem 3
How much larger is 69³ than 59³?
69³ – 59³ = 180,389.
Explanation
First, find the cube of 69³, which is 328,509
Next, find the cube of 59³, which is 148,120
Now, find the difference between them using the subtraction method. 328,509 – 148,120 = 180,389
Therefore, 69³ is 180,389 larger than 59³.
Problem 4
If a cube with a side length of 69 cm is compared to a cube with a side length of 19 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 69 cm is 328,509 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 69 means multiplying 69 by itself three times: 69 × 69 = 4,761, and then 4,761 × 69 = 328,509.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 328,509 cm³.
Problem 5
Estimate the cube of 68.9 using the cube of 69.
The cube of 68.9 is approximately 328,509.
Explanation
First, identify the cube of 69, The cube of 69 is 69³ = 328,509.
Since 68.9 is only a tiny bit less than 69, the cube of 68.9 will be almost the same as the cube of 69.
The cube of 68.9 is approximately 328,509 because the difference between 68.9 and 69 is very small.
So, we can approximate the value as 328,509.
FAQs on Cube of 69
1.What are the perfect cubes up to 69?
2.How do you calculate 69³?
3.What is the meaning of 69³?
4.What is the cube root of 69?
5.Is 69 a perfect cube?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 69?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 69?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube of 69
- 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, such as 1³, 2³, 3³, etc.
- Volume of a Cube: The amount of space enclosed within a cube, calculated as the cube of its side length (Side³).
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About BrightChamps in Saudi Arabia
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.
