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Last updated on May 30th, 2025

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Cube of 13

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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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 13.

Cube of 13 for Bahraini Students
Professor Greenline from BrightChamps

Cube of 13

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 multiplying a negative number by itself three times results in a negative number.

 

The cube of 13 can be written as 13³, which is the exponential form. Or it can also be written in arithmetic form as 13 × 13 × 13.

 

cube of 13

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How to Calculate the Value of Cube of 13

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.

 

  1. By Multiplication Method
  2. Using a Formula
  3. Using a Calculator
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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. 13³ = 13 × 13 × 13

 

Step 2: You get 2,197 as the answer. Hence, the cube of 13 is 2,197.

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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 13 into two parts, as 10 and 3. Let a = 10 and b = 3, so a + b = 13

 

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

 

Step 3: Calculate each term

 

a³ = 10³

 

3a²b = 3 × 10² × 3

 

3ab² = 3 × 10 × 3²

 

b³ = 3³

 

Step 4: Add all the terms together:

 

(a + b)³ = a³ + 3a²b + 3ab² + b³

 

(10 + 3)³ = 10³ + 3 × 10² × 3 + 3 × 10 × 3² + 3³

 

13³ = 1,000 + 900 + 270 + 27

 

13³ = 2,197

 

Step 5: Hence, the cube of 13 is 2,197.

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Using a Calculator

To find the cube of 13 using a calculator, input the number 13 and use the cube function (if available) or multiply 13 × 13 × 13. This operation calculates the value of 13³, resulting in 2,197. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 1 followed by 3

 

Step 3: If the calculator has a cube function, press it to calculate 13³.

 

Step 4: If there is no cube function on the calculator, simply multiply 13 three times manually.

 

Step 5: The calculator will display 2,197.

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Tips and Tricks for the Cube of 13

  • 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 13

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

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Incorrect Multiplication

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Kids might multiply the numbers only twice. That is, 13 × 13 and not 13 × 13 × 13. Always remember that 13³ = 13 × 13 × 13.

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Solved Examples on Cube of 13

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Problem 1

What is the cube and cube root of 13?

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The cube of 13 is 2,197 and the cube root of 13 is approximately 2.351.

Explanation

First, let’s find the cube of 13.

 

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 13³ = 2,197

 

Next, we must find the cube root of 13 We know that cube root of a number ‘x’, such that ³√x = y Where ‘x’ is the given number, and y is the cube root value of the number

 

So, we get ³√13 ≈ 2.351

 

Hence the cube of 13 is 2,197 and the cube root of 13 is approximately 2.351.

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Problem 2

If the side length of the cube is 13 cm, what is the volume?

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The volume is 2,197 cm³.

Explanation

Use the volume formula for a cube V = Side³.

 

Substitute 13 for the side length: V = 13³ = 2,197 cm³.

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Problem 3

How much larger is 13³ than 10³?

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13³ – 10³ = 1,197.

Explanation

First find the cube of 13³, that is 2,197

 

Next, find the cube of 10³, which is 1,000

 

Now, find the difference between them using the subtraction method. 2,197 – 1,000 = 1,197

 

Therefore, the 13³ is 1,197 larger than 10³.

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Problem 4

If a cube with a side length of 13 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 13 cm is 2,197 cm³.

Explanation

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

 

Cubing 13 means multiplying 13 by itself three times: 13 × 13 = 169, and then 169 × 13 = 2,197.

 

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

 

Therefore, the volume of the cube is 2,197 cm³.

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Problem 5

Estimate the cube of 12.9 using the cube of 13.

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The cube of 12.9 is approximately 2,197.

Explanation

First, identify the cube of 13. The cube of 13 is 13³ = 2,197.

 

Since 12.9 is only a tiny bit less than 13, the cube of 12.9 will be almost the same as the cube of 13.

 

The cube of 12.9 is approximately 2,197 because the difference between 12.9 and 13 is very small.

 

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

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FAQs on Cube of 13

1.What are the perfect cubes up to 13?

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2.How do you calculate 13³?

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3.What is the meaning of 13³?

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4.What is the cube root of 13?

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5.Is 13 a perfect cube?

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

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7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube of 13?

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8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 13?

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

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Professor Greenline from BrightChamps

Important Glossaries for Cube of 13

  • 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.

 

  • Multiplication Method: A method used to find the product of numbers by multiplying them repeatedly.

 

  • Cube Root: The cube root of a number is a value that when multiplied by itself three times gives the original number. For example, the cube root of 8 is 2.
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About BrightChamps in Bahrain

At BrightChamps, algebra is more than just digits—it unlocks endless opportunities! We strive to help kids all across Bahrain develop key math skills, focusing today on the Cube of 13 with an exciting look at cubes—in a lively, clear, and enjoyable way. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, tracking football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence in everyday challenges. Our interactive lessons make math easy and fun. Because kids in Bahrain learn differently, we tailor our teaching to each child’s learning style. From Manama’s lively city life to Bahrain’s peaceful beaches, BrightChamps makes algebra come alive, making it exciting and relevant across Bahrain. 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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