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Last updated on June 30th, 2025

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Cube of 1297

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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 the cube of 1297.

Cube of 1297 for Saudi Students
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Cube of 1297

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 1297 can be written as 1297³, which is the exponential form. Or it can also be written in arithmetic form as 1297 × 1297 × 1297.

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How to Calculate the Value of Cube of 1297

In order to check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (a³), or by using a calculator.

 

These three methods will help calculate the cube of numbers faster and easier without feeling confused or stuck while evaluating the answers.

 

By Multiplication Method Using a Formula Using a Calculator

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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. 1297³ = 1297 × 1297 × 1297

 

Step 2: Perform the multiplication to get the answer. Hence, the cube of 1297 is 2,180,707,473.

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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 1297 into two parts, as a and b. Let a = 1300 and b = -3, so a + b = 1297

 

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

 

Step 3: Calculate each term a³ = 1300³ 3a²b = 3 × 1300² × (-3) 3ab² = 3 × 1300 × (-3)² b³ = (-3)³

 

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (1300 - 3)³ = 1300³ + 3 × 1300² × (-3) + 3 × 1300 × 9 + (-27) 1297³ = 2,197,000,000 - 15,210,000 + 35,100 - 27 1297³ = 2,180,707,473

 

Step 5: Hence, the cube of 1297 is 2,180,707,473.

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Using a Calculator

To find the cube of 1297 using a calculator, input the number 1297 and use the cube function (if available) or multiply 1297 × 1297 × 1297.

 

This operation calculates the value of 1297³, resulting in 2,180,707,473.

 

It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Input 1297

 

Step 3: If the calculator has a cube function, press it to calculate 1297³.

 

Step 4: If there is no cube function on the calculator, simply multiply 1297 three times manually.

 

Step 5: The calculator will display 2,180,707,473. 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.

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Common Mistakes to Avoid When Calculating the Cube of 1297

There are some typical errors that individuals might make during the process of cubing a number.

 

Let us take a look at five of the major mistakes that might occur:

Mistake 1

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Incorrect Multiplication

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Individuals might multiply the numbers only twice. That is, 1297 × 1297 and not 1297 × 1297 × 1297. Always remember that 1297³ = 1297 × 1297 × 1297.

Mistake 2

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Misunderstanding the Cube Formula

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There is a possibility that individuals might be confused between the formulas of square numbers and cube numbers.

 

The square number formula is (a + b)² and the cube number formula is (a + b)³.

 

Always review the formula for the difference between squaring and cubing.

Mistake 3

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Calculator Misuse

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Individuals might press the wrong buttons, 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 in steps.

Mistake 4

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Misplacing Zeros

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Misplacing zeros during manual multiplication, leads to incorrect results. For this, always double-check your answers.

Mistake 5

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Ignoring the Binomial Formula

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Individuals might attempt to split 1297 into two numbers 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.

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Solved Examples on Cube of 1297

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Problem 1

What is the cube and cube root of 1297?

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The cube of 1297 is 2,180,707,473 and the cube root of 1297 is approximately 10.861.

Explanation

First, let’s find the cube of 1297. 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 1297³ = 2,180,707,473. Next, we must find the cube root of 1297.

 

We know that the 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 ∛1297 ≈ 10.861.

 

Hence, the cube of 1297 is 2,180,707,473 and the cube root of 1297 is approximately 10.861.

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Problem 2

If the side length of the cube is 1297 cm, what is the volume?

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The volume is 2,180,707,473 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 1297 for the side length: V = 1297³ = 2,180,707,473 cm³.

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Problem 3

How much larger is 1297³ than 1000³?

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1297³ – 1000³ = 1,180,707,473.

Explanation

First, find the cube of 1297³, that is 2,180,707,473. Next, find the cube of 1000³, which is 1,000,000,000.

 

Now, find the difference between them using the subtraction method. 2,180,707,473 – 1,000,000,000 = 1,180,707,473.

 

Therefore, 1297³ is 1,180,707,473 larger than 1000³.

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Problem 4

If a cube with a side length of 1297 cm is compared to a cube with a side length of 3 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 1297 cm is 2,180,707,473 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

 

Cubing 1297 means multiplying 1297 by itself three times: 1297 × 1297 = 1,682,209, and then 1,682,209 × 1297 = 2,180,707,473.

 

The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.

 

Therefore, the volume of the cube is 2,180,707,473 cm³.

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Problem 5

Estimate the cube of 1300 using the cube of 1297.

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The cube of 1300 is approximately 2,197,000,000.

Explanation

First, identify the cube of 1297. The cube of 1297 is 1297³ = 2,180,707,473.

 

Since 1300 is only slightly larger than 1297, the cube of 1300 will be slightly larger than the cube of 1297.

 

The cube of 1300 is approximately 2,197,000,000 because the difference between 1297 and 1300 is small.

 

So, we can approximate the value as 2,197,000,000.

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FAQs on Cube of 1297

1.What are the perfect cubes up to 1297?

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2.How do you calculate 1297³?

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3.What is the meaning of 1297³?

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4.What is the cube root of 1297?

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5.Is 1297 a perfect cube?

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6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?

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7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 1297?

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8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 1297?

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9.Does learning Algebra support future career opportunities for students in Saudi Arabia?

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Important Glossaries for Cube of 1297

  • 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: It is a number that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.

 

  • Volume of a Cube: It is the amount of space occupied by a cube, calculated as the cube of its side length (Side³).
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About BrightChamps inSaudi Arabia

At BrightCHAMPS, algebra means more than just figures it unlocks endless opportunities! Our mission is to support kids all across Saudi Arabia in learning key math concepts, including today’s focus on the Cube of 1297 with a special highlight on cubes in a fun, clear, and engaging way. Whether your child is figuring out the speed of a roller coaster at Riyadh’s Al Hokair Land, following scores at a local football match, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence for everyday challenges. Our interactive lessons make learning simple and fun. Since kids in Saudi Arabia have different ways of learning, we customize our approach to each child’s style. From Riyadh’s bustling streets to Jeddah’s historic sites, BrightCHAMPS brings algebra to life, making it exciting and relevant across Saudi Arabia. Let’s make cubes a fun part of every child’s math journey!
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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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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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