100 LearnersLast updated on June 3rd, 2025
Cube of 67
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 67.
Cube of 67
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 67 can be written as 67³, which is the exponential form. Or it can also be written in arithmetic form as, 67 × 67 × 67.
How to Calculate the Value of Cube of 67
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
- 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. 67³ = 67 × 67 × 67
Step 2: You get 300,763 as the answer.
Hence, the cube of 67 is 300,763.
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 67 into two parts, as 60 and 7.
Let a = 60 and b = 7, so a + b = 67
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 60³ , 3a²b = 3 × 60² × 7 , 3ab² = 3 × 60 × 7² , b³ = 7³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(60 + 7)³ = 60³ + 3 × 60² × 7 + 3 × 60 × 7² + 7³
67³ = 216000 + 75600 + 8820 + 343 67³
= 300,763
Step 5: Hence, the cube of 67 is 300,763.
Using a Calculator
To find the cube of 67 using a calculator, input the number 67 and use the cube function (if available) or multiply 67 × 67 × 67. This operation calculates the value of 67³, resulting in 300,763. 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 7
Step 3: If the calculator has a cube function, press it to calculate 67³.
Step 4: If there is no cube function on the calculator, simply multiply 67 three times manually.
Step 5: The calculator will display 300,763.
Tips and Tricks for the Cube of 67
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 67
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, 67 × 67 and not 67 × 67 × 67. Always remember that 67³ = 67 × 67 × 67.
Solved Examples on Cube of 67
Problem 1
What is the cube and cube root of 67?
The cube of 67 is 300,763 and the cube root of 67 is approximately 4.041.
Explanation
First, let’s find the cube of 67.
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 67³ = 300,763
Next, we must find the cube root of 67
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√67 ≈ 4.041
Hence, the cube of 67 is 300,763 and the cube root of 67 is approximately 4.041.
Problem 2
If the side length of the cube is 67 cm, what is the volume?
The volume is 300,763 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 67 for the side length: V = 67³ = 300,763 cm³.
Problem 3
How much larger is 67³ than 60³?
67³ – 60³ = 84,763.
Explanation
First, find the cube of 67³, that is 300,763
Next, find the cube of 60³, which is 216,000
Now, find the difference between them using the subtraction method.
300,763 – 216,000 = 84,763
Therefore, 67³ is 84,763 larger than 60³.
Problem 4
If a cube with a side length of 67 cm is compared to a cube with a side length of 7 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 67 cm is 300,763 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 67 means multiplying 67 by itself three times: 67 × 67 = 4,489, and then 4,489 × 67 = 300,763.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 300,763 cm³.
Problem 5
Estimate the cube of 66.9 using the cube of 67.
The cube of 66.9 is approximately 300,763.
Explanation
First, identify the cube of 67.
The cube of 67 is 67³ = 300,763.
Since 66.9 is only a tiny bit less than 67, the cube of 66.9 will be almost the same as the cube of 67.
The cube of 66.9 is approximately 300,763 because the difference between 66.9 and 67 is very small.
So, we can approximate the value as 300,763.
FAQs on Cube of 67
1.What are the perfect cubes up to 67?
2.How do you calculate 67³?
3.What is the meaning of 67³?
4.What is the cube root of 67?
5.Is 67 a perfect cube?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Cube of 67?
8.How do technology and digital tools in India support learning Algebra and Cube of 67?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Cube of 67
- 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. It is denoted as ³√x.
- Perfect Cube: A perfect cube is a number that can be expressed as the cube of an integer.
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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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