103 LearnersLast updated on June 30th, 2025
Cube of 1275
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 the cube of 1275.
Cube of 1275
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.
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When you cube a positive number, the result is always positive.
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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 1275 can be written as:
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Exponential form: 1275³
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Arithmetic form: 1275 × 1275 × 1275
How to Calculate the Value of Cube of 1275
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.
1275³ = 1275 × 1275 × 1275
Step 2: You get 2,075,171,875 as the answer.
Hence, the cube of 1275 is 2,075,171,875.
Using a Formula (\(a^3\))
The formula (a + b)³ is a binomial formula for finding the cube of a number. It expands as:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Step 1: Split the number 1275 into two parts:
a = 1200, b = 75, so a + b = 1275
Step 2: Apply the formula:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term:
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a³ = 1200³ = 1,728,000,000
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3a²b = 3 × 1200² × 75 = 324,000,000
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3ab² = 3 × 1200 × 75² = 202,500,000
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b³ = 75³ = 421,875
Step 4: Add all the terms:
(1200 + 75)³ = 1,728,000,000 + 324,000,000 + 202,500,000 + 421,875
1275³ = 2,075,171,875
Step 5:
Hence, the cube of 1275 is 2,075,171,875.
Using a Calculator
To find the cube of 1275 using a calculator, input the number 1275 and use the cube function (if available) or multiply:
1275 × 1275 × 1275.
This operation calculates 1275³, resulting in 2,075,171,875.
It’s a quick way to determine the cube without manual computation.
Steps:
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Ensure the calculator is functioning properly.
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Press 1, 2, 7, 5.
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If the calculator has a cube function, press it to compute 1275³.
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If there is no cube function, multiply:
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First: 1275 × 1275
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Then multiply that result by 1275 again.
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The calculator will display 2,075,171,875.
Tips and Tricks for the Cube of 1275
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 1275
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,
1275 × 1275,
and not
1275 × 1275 × 1275.
Always remember that
1275³ = 1275 × 1275 × 1275.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility that kids might be confused between the formulas of square numbers and cube numbers.
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The square number formula is:
(a + b)² = a² + 2ab + b² -
The cube number formula is:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Always review the formula to understand the difference between squaring and cubing.
Mistake 3
Calculator Misuse
Kids might press the wrong buttons, such as using the square (x²) function instead of the cube (x³) function, or they might skip steps in manual multiplication.
Always double-check your inputs on the calculator, and if it lacks a cube function, perform the multiplication step by step to ensure accuracy.
Mistake 4
Misplacing Zeros
Misplacing zeros during manual multiplication leads to incorrect results. For this, kids should always double-check their answers.
Mistake 5
Ignoring the Binomial Formula
Kids might attempt to split the 1275 into 1200 + 75 but not apply the correct binomial expansion. In order to avoid this, carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 1275
Problem 1
What is the cube and cube root of 1275?
The cube of 1275 is 2,075,171,875 and the cube root of 1275 is approximately 10.762.
Explanation
First, let’s find the cube of 1275.
We know that the cube of a number is given by:
x³ = y,
where x is the given number, and y is the cubed value of that number.
So,
1275³ = 2,075,171,875.
Next, we find the cube root of 1275.
The cube root of a number is given by:
∛x = y,
where x is the given number, and y is the cube root.
So,
∛1275 ≈ 10.762.
Hence, the cube of 1275 is 2,075,171,875, and the cube root of 1275 is approximately 10.762.
Problem 2
If the side length of the cube is 1275 cm, what is the volume?
The volume is 2,075,171,875 cm³.
Explanation
Use the volume formula for a cube:
V = Side³
Substitute 1275 for the side length:
V = 1275³ = 2,075,171,875 cm³
Problem 3
How much larger is \(1275^3\) than \(1200^3\)?
1275³ − 1200³ = 347,171,875
Explanation
First, find the cube of 1275:
1275³ = 2,075,171,875
Next, find the cube of 1200:
1200³ = 1,728,000,000
Now, find the difference using subtraction:
2,075,171,875 − 1,728,000,000 = 347,171,875
Therefore, 1275³ is 347,171,875 larger than 1200³.
Problem 4
If a cube with a side length of 1275 cm is compared to a cube with a side length of 75 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1275 cm is 2,075,171,875 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1275 means multiplying 1275 by itself three times:
1275 × 1275 = 1,625,625
then
1,625,625 × 1275 = 2,075,171,875
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,075,171,875 cm³
Problem 5
Estimate the cube of 1274 using the cube of 1275.
The cube of 1274 is approximately 2,075,171,875.
Explanation
First, identify the cube of 1275:
1275³ = 2,075,171,875.
Since 1274 is only a tiny bit less than 1275, the cube of 1274 will be almost the same as the cube of 1275.
The cube of 1274 is approximately 2,075,171,875 because the difference between 1274 and 1275 is very small.
So, we can use this value as an approximation.
FAQs on Cube of 1275
1.What are the perfect cubes up to 1275?
2.How do you calculate \(1275^3\)?
3.What is the meaning of \(1275^3\)?
4.What is the cube root of 1275?
5.Is 1275 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 1275?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 1275?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube of 1275
- 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 indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 = 8.
- Perfect Cube:A number that can be expressed as the product of an integer multiplied by itself twice more, such as 1, 8, 27, etc.
- Volume of a Cube:The space occupied by a cube, calculated by raising the side length to the power of three (side³).
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Jaskaran Singh Saluja
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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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