101 LearnersLast updated on June 3rd, 2025
Cube of 65
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 65.
Cube of 65
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 65 can be written as 65³, which is the exponential form. Or it can also be written in arithmetic form as 65 × 65 × 65.
How to Calculate the Value of Cube of 65
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
- 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.
65³ = 65 × 65 × 65
Step 2: You get 274,625 as the answer.
Hence, the cube of 65 is 274,625.
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 65 into two parts. Let a = 60 and b = 5, so a + b = 65
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 60³ , 3a²b = 3 × 60² × 5 , 3ab² = 3 × 60 × 5² , b³ = 5³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³ (60 + 5)³
= 60³ + 3 × 60² × 5 + 3 × 60 × 5² + 5³
65³ = 216,000 + 54,000 + 4,500 + 125 65³
= 274,625
Step 5: Hence, the cube of 65 is 274,625.
Using a Calculator
To find the cube of 65 using a calculator, input the number 65 and use the cube function (if available) or multiply 65 × 65 × 65. This operation calculates the value of 65³, resulting in 274,625. 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 5
Step 3: If the calculator has a cube function, press it to calculate 65³.
Step 4: If there is no cube function on the calculator, simply multiply 65 three times manually.
Step 5: The calculator will display 274,625.
Tips and Tricks for the Cube of 65
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 65
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, 65 × 65 and not 65 × 65 × 65. Always remember that 65³ = 65 × 65 × 65.
Solved Examples on Cube of 65
Problem 1
What is the cube and cube root of 65?
The cube of 65 is 274,625 and the cube root of 65 is approximately 4.0207.
Explanation
First, let’s find the cube of 65.
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 65³ = 274,625
Next, we find the cube root of 65
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 ∛65 ≈ 4.0207
Hence, the cube of 65 is 274,625 and the cube root of 65 is approximately 4.0207.
Problem 2
If the side length of the cube is 65 cm, what is the volume?
The volume is 274,625 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 65 for the side length: V = 65³ = 274,625 cm³.
Problem 3
How much larger is 65³ than 50³?
65³ – 50³ = 149,625.
Explanation
First, find the cube of 65³, which is 274,625
Next, find the cube of 50³, which is 125,000
Now, find the difference between them using the subtraction method.
274,625 – 125,000 = 149,625
Therefore, 65³ is 149,625 larger than 50³.
Problem 4
If a cube with a side length of 65 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 65 cm is 274,625 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 65 means multiplying 65 by itself three times: 65 × 65 = 4,225, and then 4,225 × 65 = 274,625.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 274,625 cm³.
Problem 5
Estimate the cube of 64.9 using the cube of 65.
The cube of 64.9 is approximately 274,625.
Explanation
First, identify the cube of 65.
The cube of 65 is 65³ = 274,625.
Since 64.9 is only a tiny bit less than 65, the cube of 64.9 will be almost the same as the cube of 65.
The cube of 64.9 is approximately 274,625 because the difference between 64.9 and 65 is very small.
So, we can approximate the value as 274,625.
FAQs on Cube of 65
1.What are the perfect cubes up to 65?
2.How do you calculate 65³?
3.What is the meaning of 65³?
4.What is the cube root of 65?
5.Is 65 a perfect cube?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of 65?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 65?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube of 65
- 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 perfect cube is an integer that is the cube of an integer.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of the side length.
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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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