101 LearnersLast updated on June 3rd, 2025
Cube of 64
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used for comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 64.
Cube of 64
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 64 can be written as 64³, which is the exponential form. Or it can also be written in arithmetic form as, 64 × 64 × 64.
How to Calculate the Value of Cube of 64
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 numbers 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. 64³ = 64 × 64 × 64
Step 2: You get 262,144 as the answer.
Hence, the cube of 64 is 262,144.
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 64 into two parts.
Let a = 60 and b = 4, so a + b = 64
Step 2: Now, apply the formula
(a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 60³ , 3a²b = 3 × 60² × 4 , 3ab² = 3 × 60 × 4² , b³ = 4³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(60 + 4)³ = 60³ + 3 × 60² × 4 + 3 × 60 × 4² + 4³
64³ = 216,000 + 43,200 + 2,880 + 64
64³ = 262,144
Step 5: Hence, the cube of 64 is 262,144.
Using a Calculator
To find the cube of 64 using a calculator, input the number 64 and use the cube function (if available) or multiply 64 × 64 × 64. This operation calculates the value of 64³, resulting in 262,144. 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 4
Step 3: If the calculator has a cube function, press it to calculate 64³.
Step 4: If there is no cube function on the calculator, simply multiply 64 three times manually.
Step 5: The calculator will display 262,144.
Tips and Tricks for the Cube of 64
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 64
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, 64 × 64 and not 64 × 64 × 64. Always remember that 64³ = 64 × 64 × 64.
Solved Examples on Cube of 64
Problem 1
What is the cube and cube root of 64?
The cube of 64 is 262,144 and the cube root of 64 is 4.
Explanation
First, let’s find the cube of 64.
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 64³ = 262,144
Next, we must find the cube root of 64
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√64 = 4
Hence, the cube of 64 is 262,144 and the cube root of 64 is 4.
Problem 2
If the side length of the cube is 64 cm, what is the volume?
The volume is 262,144 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 64 for the side length: V = 64³ = 262,144 cm³.
Problem 3
How much larger is 64³ than 60³?
64³ – 60³ = 46,144.
Explanation
First, find the cube of 64³, that is 262,144
Next, find the cube of 60³, which is 216,000
Now, find the difference between them using the subtraction method.
262,144 – 216,000 = 46,144
Therefore, 64³ is 46,144 larger than 60³.
Problem 4
If a cube with a side length of 64 cm is compared to a cube with a side length of 16 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 64 cm is 262,144 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 64 means multiplying 64 by itself three times: 64 × 64 = 4,096, and then 4,096 × 64 = 262,144.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 262,144 cm³.
Problem 5
Estimate the cube 63.9 using the cube of 64.
The cube of 63.9 is approximately 262,144.
Explanation
First, identify the cube of 64.
The cube of 64 is 64³ = 262,144.
Since 63.9 is only a tiny bit less than 64, the cube of 63.9 will be almost the same as the cube of 64.
The cube of 63.9 is approximately 262,144 because the difference between 63.9 and 64 is very small.
So, we can approximate the value as 262,144.
FAQs on Cube of 64
1.What are the perfect cubes up to 64?
2.How do you calculate 64³?
3.What is the meaning of 64³?
4.What is the cube root of 64?
5.Is 64 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 64?
8.How do technology and digital tools in United States support learning Algebra and Cube of 64?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 64
- 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.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
- 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.
