Cube of -13
2026-02-28 11:40 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-minus-13

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Last updated on August 5, 2025

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

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.

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

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.

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.

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.

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:

Problem 1

What is the cube and cube root of -13?

Okay, lets begin

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.

Well explained 👍

Problem 2

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

Okay, lets begin

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?

Okay, lets begin

(-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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Estimate the cube of -12.9 using the cube of -13.

Okay, lets begin

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.

Well explained 👍

FAQs on Cube of -13

1.What are the perfect cubes up to 13?

The perfect cubes up to 13 are 1, 8, and 27.

2.How do you calculate (-13)^3?

To calculate (-13)^3, use the multiplication method, -13 × -13 × -13, which equals -2,197.

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

(-13)^3 means -13 multiplied by itself three times, or -13 × -13 × -13.

4.What is the cube root of -13?

The cube root of -13 is approximately -2.351.

5.Is -13 a perfect cube?

No, -13 is not a perfect cube because no integer multiplied by itself three times equals -13.

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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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.

Fun Fact

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