102 LearnersLast updated on June 3rd, 2025
Cube of 60
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 cubes of 60.
Cube of 60
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 60 can be written as 60³, which is the exponential form. Or it can also be written in arithmetic form as, 60 × 60 × 60.
How to Calculate the Value of Cube of 60
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.
60³ = 60 × 60 × 60
Step 2: You get 216,000 as the answer.
Hence, the cube of 60 is 216,000.
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 60 into two parts. Let a = 50 and b = 10, so a + b = 60
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 50³ , 3a²b = 3 × 50² × 10 , 3ab² = 3 × 50 × 10² , b³ = 10³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(50 + 10)³ = 50³ + 3 × 50² × 10 + 3 × 50 × 10² + 10³
60³ = 125,000 + 75,000 + 15,000 + 1,000 60³
= 216,000
Step 5: Hence, the cube of 60 is 216,000.
Using a Calculator
To find the cube of 60 using a calculator, input the number 60 and use the cube function (if available) or multiply 60 × 60 × 60. This operation calculates the value of 60³, resulting in 216,000. 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 0
Step 3: If the calculator has a cube function, press it to calculate 60³.
Step 4: If there is no cube function on the calculator, simply multiply 60 three times manually.
Step 5: The calculator will display 216,000.
Tips and Tricks for the Cube of 60
- 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 60
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, 60 × 60 and not 60 × 60 × 60. Always remember that 60³ = 60 × 60 × 60.
Solved Examples on Cube of 60
Problem 1
What is the cube and cube root of 60?
The cube of 60 is 216,000 and the cube root of 60 is approximately 3.914.
Explanation
First, let’s find the cube of 60.
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 60³ = 216,000
Next, we must find the cube root of 60 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 ∛60 ≈ 3.914
Hence, the cube of 60 is 216,000 and the cube root of 60 is approximately 3.914.
Problem 2
If the side length of the cube is 60 cm, what is the volume?
The volume is 216,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 60 for the side length: V = 60³ = 216,000 cm³.
Problem 3
How much larger is 60³ than 50³?
60³ – 50³ = 91,000.
Explanation
First find the cube of 60³, that is 216,000
Next, find the cube of 50³, which is 125,000
Now, find the difference between them using the subtraction method.
216,000 – 125,000 = 91,000
Therefore, the 60³ is 91,000 larger than 50³.
Problem 4
If a cube with a side length of 60 cm is compared to a cube with a side length of 20 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 60 cm is 216,000 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 60 means multiplying 60 by itself three times: 60 × 60 = 3,600, and then 3,600 × 60 = 216,000.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 216,000 cm³.
Problem 5
Estimate the cube 59.9 using the cube 60.
The cube of 59.9 is approximately 216,000.
Explanation
First, identify the cube of 60, The cube of 60 is 60³ = 216,000.
Since 59.9 is only a tiny bit less than 60, the cube of 59.9 will be almost the same as the cube of 60.
The cube of 59.9 is approximately 216,000 because the difference between 59.9 and 60 is very small.
So, we can approximate the value as 216,000.
FAQs on Cube of 60
1.What are the perfect cubes up to 60?
2.How do you calculate 60³?
3.What is the meaning of 60³?
4.What is the cube root of 60?
5.Is 60 a perfect cube?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Cube of 60?
8.How do technology and digital tools in Oman support learning Algebra and Cube of 60?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube of 60
- 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 calculated as the cube of its side length, expressed as 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.
