101 LearnersLast updated on July 1st, 2025
Cube of 1298
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 1298.
Cube of 1298
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 1298 can be written as (12983), which is the exponential form.
Or it can also be written in arithmetic form as, 1298 × 1298 × 1298
How to Calculate the Value of Cube of 1298
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 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.
1298³ = 1298 × 1298 × 1298
Step 2: You get 2,185,034,392 as the answer.
Hence, the cube of 1298 is 2,185,034,392.
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 1298 into two parts:
a = 1290 and b = 8, so a + b = 1298.
Step 2: Now, apply the formula:
(a + b)³ = a³ + 3a²b + 3ab² + b³.
Step 3: Calculate each term:
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a³ = 1290³
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3a²b = 3 × 1290² × 8
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3ab² = 3 × 1290 × 8²
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b³ = 8³
Step 4: Add all the terms together:
1298³ = 1290³ + 3 × 1290² × 8 + 3 × 1290 × 8² + 8³.
Step 5: Hence, the cube of 1298 is 2,185,034,392.
Using a Calculator
To find the cube of 1298 using a calculator, input the number 1298 and use the cube function (if available) or multiply:
1298 × 1298 × 1298.
This operation calculates the value of 1298³, resulting in 2,185,034,392. 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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Enter 1298.
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If the calculator has a cube function, press it to calculate 1298³.
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If there is no cube function on the calculator, simply multiply 1298 three times manually.
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The calculator will display 2,185,034,392.
Tips and Tricks for the Cube of 1298
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 1298
There are some typical errors that might occur 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 an error in multiplying the numbers only twice, that is,
1298 × 1298,
and not
1298 × 1298 × 1298.
Always remember that:
1298³ = 1298 × 1298 × 1298.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility of confusion between the formulas of square numbers and cube numbers.
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The square number formula is: (a + b)²
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The cube number formula is: (a + b)³
Always review the formulas to understand the difference between squaring and cubing.
Mistake 3
Calculator Misuse
There might be errors such as using the square (x²) function instead of the cube (x³) function, or skipping 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.
Mistake 4
Misplacing Zeros
Misplacing zeros during manual multiplication leads to incorrect results like 2,185,034,39 instead of 2,185,034,392. Always double-check your answers.
Mistake 5
Ignoring the Binomial Formula
Attempting to split the number incorrectly or not applying the correct binomial expansion. Carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 1298
Problem 1
What is the cube and cube root of 1298?
The cube of 1298 is 2,185,034,392 and the cube root of 1298 is approximately 10.776.
Explanation
First, let’s find the cube of 1298.
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, we get:
1298³ = 2,185,034,392.
Next, we must find the cube root of 1298.
We know that the cube root of a number is given by:
∛x = y
where x is the given number, and y is the cube root value of the number.
So, we get:
∛1298 ≈ 10.776.
Hence, the cube of 1298 is 2,185,034,392, and the cube root of 1298 is approximately 10.776.
Problem 2
If the side length of the cube is 1298 cm, what is the volume?
The volume is 2,185,034,392 cm\(^3\).
Explanation
Use the volume formula for a cube:
V = Side³
Substitute 1298 for the side length:
V = 1298³ = 2,185,034,392 cm³
Problem 3
How much larger is \(1298^3\) than \(1200^3\)?
1298³ − 1200³ = 608,034,392
Explanation
First, find the cube of 1298:
1298³ = 2,185,034,392
Next, find the cube of 1200:
1200³ = 1,577,000,000
Now, find the difference using the subtraction method:
2,185,034,392 − 1,577,000,000 = 608,034,392
Therefore, 1298³ is 608,034,392 larger than 1200³.
Problem 4
If a cube with a side length of 1298 cm is compared to a cube with a side length of 800 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1298 cm is 2,185,034,392 cm\(^3\).
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1298 means multiplying 1298 by itself three times:
1298 × 1298 × 1298 = 2,185,034,392.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,185,034,392 cm³.
Problem 5
Estimate the cube of 1300 using the cube of 1298.
The cube of 1300 is approximately 2,197,000,000.
Explanation
First, identify the cube of 1298:
The cube of 1298 is 1298³ = 2,185,034,392.
Since 1300 is slightly more than 1298, the cube of 1300 will be slightly more than the cube of 1298.
The cube of 1300 is approximately 2,197,000,000, because it is only a bit larger than 1298.
So, we can approximate the value as 2,197,000,000.
FAQs on Cube of 1298
1.What are the perfect cubes up to 1298?
2.How do you calculate1298³?
3.What is the meaning of 1298³?
4.What is the cube root of 1298?
5.Is 1298 a perfect cube?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Cube of 1298?
8.How do technology and digital tools in Qatar support learning Algebra and Cube of 1298?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Cube of 1298
- 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 = 8.
- Multiplication Method:A process in mathematics used to find the product of numbers by combining them through repeated addition.
- Perfect Cube:A number that can be expressed as the cube of an integer.
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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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