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Last updated on May 26th, 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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of -13.

Cube of -13 for US Students
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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 a negative number multiplied by itself three times results in a negative number. The cube of -13 can be written as (-13)^3, which is the exponential form. Or it can also be written in arithmetic form as, -13 × -13 × -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, such as the multiplication method, a factor formula (a^3), 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

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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. (-13)^3 = -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 (a^3)

The formula (a + b)^3 is a binomial formula for finding the cube of a number. The formula is expanded as a^3 + 3a^2b + 3ab^2 + b^3. 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 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-10)^3 3a^2b = 3 × (-10)^2 × -3 3ab^2 = 3 × -10 × (-3)^2 b^3 = (-3)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-10 + -3)^3 = (-10)^3 + 3 × (-10)^2 × -3 + 3 × -10 × (-3)^2 + (-3)^3 (-13)^3 = -1,000 - 900 + 270 - 27 (-13)^3 = -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 (-13)^3, 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 (-13)^3. 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 (-13)^3 = -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 the cube of a number, such that x^3 = y Where x is the given number, and y is the cubed value of that number So, we get (-13)^3 = -2,197 Next, we must find the cube root of -13 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 ∛-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 a cube is -13 cm, what is the volume?

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A cube cannot have a negative side length, so this is a theoretical scenario. The volume would be -2,197 cm³.

Explanation

Use the volume formula for a cube V = Side^3. Substitute -13 for the side length: V = (-13)^3 = -2,197 cm³. Note: In real-life scenarios, a cube cannot have negative dimensions.

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Problem 3

How much larger is (-13)^3 than (-10)^3?

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(-13)^3 – (-10)^3 = -1,197.

Explanation

First find the cube of (-13)^3, which is -2,197 Next, find the cube of (-10)^3, which is -1,000 Now, find the difference between them using the subtraction method. -2,197 - (-1,000) = -1,197 Therefore, (-13)^3 is -1,197 larger than (-10)^3.

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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 10 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 10 cm is 1,000 cm³, which is larger than the theoretical -2,197 cm³.

Explanation

To find the volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 10 means multiplying 10 by itself three times: 10 × 10 = 100, and then 100 × 10 = 1,000. The unit of volume is cubic centimeters (cm³). Therefore, the real-life cube volume is 1,000 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 (-13)^3 = -2,197. Since -12.9 is only a tiny bit more 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 (-13)^3?

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3.What is the meaning of (-13)^3?

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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 United States make better decisions in daily life?

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

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

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

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Important Glossaries for Cube of -13

Binomial Formula: An algebraic expression used to expand the powers of a sum, 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: 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, 2^3 represents 2 × 2 × 2 equals 8. Negative Numbers: Numbers less than zero, often used to represent loss, deficiency, or opposite directions. Perfect Cube: A number that can be expressed as the cube of an integer.

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About BrightChamps in United States

At BrightChamps, we believe algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to support kids all across the United States in mastering essential math concepts, like today’s focus on the Cube of -13, especially the fascinating world of cubes—in a way that’s engaging, clear, and enjoyable. Whether your child is calculating how quickly a roller coaster zooms through Disney World, tracking scores at a Little League baseball game, or budgeting their allowance for new gadgets, understanding algebra builds the confidence they need for daily life. Our hands-on lessons make math both accessible and fun. Since children in the USA learn in diverse ways, we customize our teaching to match each student’s learning style. From the energetic streets of New York City to the sunny beaches of California, BrightChamps brings algebra to life, making it exciting and relevant across America. Let’s make cubes an exciting 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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