102 LearnersLast updated on June 3rd, 2025
Cube of 261
When a number is multiplied by itself three times, 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 the cube of 261.
Cube of 261
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 261 can be written as 261³, which is the exponential form.
Or it can also be written in arithmetic form as, 261 × 261 × 261.
How to Calculate the Value of Cube of 261
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 in cubing numbers faster and easier without confusion or errors during evaluation.
- 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 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. 261³ = 261 × 261 × 261
Step 2: You get 17,766,981 as the answer. Hence, the cube of 261 is 17,766,981.
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 261 into two parts, as 250 and 11. Let a = 250 and b = 11, so a + b = 261
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 250³ 3a²b = 3 × 250² × 11 3ab² = 3 × 250 × 11² b³ = 11³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (250 + 11)³ = 250³ + 3 × 250² × 11 + 3 × 250 × 11² + 11³ 261³ = 15,625,000 + 2,062,500 + 82,500 + 1,331 261³ = 17,766,981
Step 5: Hence, the cube of 261 is 17,766,981.
Using a Calculator
To find the cube of 261 using a calculator, input the number 261 and use the cube function (if available) or multiply 261 × 261 × 261. This operation calculates the value of 261³, resulting in 17,766,981. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2, 6, followed by 1
Step 3: If the calculator has a cube function, press it to calculate 261³.
Step 4: If there is no cube function on the calculator, simply multiply 261 three times manually.
Step 5: The calculator will display 17,766,981.
Tips and Tricks for the Cube of 261
- 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 261
There are some typical errors that might be made during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:
Mistake 1
Incorrect Multiplication
There might be a mistake of multiplying the numbers only twice. That is, 261 × 261 and not 261 × 261 × 261. Always remember that 261³ = 261 × 261 × 261.
Solved Examples on Cube of 261
Problem 1
What is the cube and cube root of 261?
The cube of 261 is 17,766,981 and the cube root of 261 is approximately 6.375.
Explanation
First, let’s find the cube of 261.
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 261³ = 17,766,981
Next, we must find the cube root of 261
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 ∛261 ≈ 6.375
Hence the cube of 261 is 17,766,981 and the cube root of 261 is approximately 6.375.
Problem 2
If the side length of a cube is 261 cm, what is the volume?
The volume is 17,766,981 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 261 for the side length: V = 261³ = 17,766,981 cm³.
Problem 3
How much larger is 261³ than 250³?
261³ – 250³ = 2,141,981.
Explanation
First find the cube of 261³, which is 17,766,981
Next, find the cube of 250³, which is 15,625,000
Now, find the difference between them using the subtraction method. 17,766,981 – 15,625,000 = 2,141,981
Therefore, 261³ is 2,141,981 larger than 250³.
Problem 4
If a cube with a side length of 261 cm is compared to a cube with a side length of 11 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 261 cm is 17,766,981 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 261 means multiplying 261 by itself three times: 261 × 261 = 68,121, and then 68,121 × 261 = 17,766,981.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 17,766,981 cm³.
Problem 5
Estimate the cube of 260.9 using the cube of 261.
The cube of 260.9 is approximately 17,766,981.
Explanation
First, identify the cube of 261,
The cube of 261 is 261³ = 17,766,981.
Since 260.9 is only a tiny bit less than 261, the cube of 260.9 will be almost the same as the cube of 261.
The cube of 260.9 is approximately 17,766,981 because the difference between 260.9 and 261 is very small.
So, we can approximate the value as 17,766,981.
FAQs on Cube of 261
1.What are the perfect cubes up to 261?
2.How do you calculate 261³?
3.What is the meaning of 261³?
4.What is the cube root of 261?
5.Is 261 a perfect cube?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube of 261?
8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 261?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for Cube of 261
- 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.
- Volume of a Cube: The amount of space inside a cube, calculated as the side length raised to the third power.
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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.
