Cube of -12
2026-02-28 19:05 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-minus-12

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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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of -12.

Cube of -12

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 -12 can be written as (-12)^3, which is the exponential form. Or it can also be written in arithmetic form as -12 × -12 × -12.

How to Calculate the Value of the Cube of -12

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 methods will help 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. (-12)^3 = -12 × -12 × -12 Step 2: You get -1,728 as the answer. Hence, the cube of -12 is -1,728.

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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 -12 into two parts, as -10 and -2. Let a = -10 and b = -2, so a + b = -12 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 × (-2) 3ab^2 = 3 × (-10) × (-2)^2 b^3 = (-2)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-10 - 2)^3 = (-10)^3 + 3 × (-10)^2 × (-2) + 3 × (-10) × (-2)^2 + (-2)^3 (-12)^3 = -1,000 - 600 - 120 - 8 (-12)^3 = -1,728 Step 5: Hence, the cube of -12 is -1,728.

Using a Calculator

To find the cube of -12 using a calculator, input the number -12 and use the cube function (if available) or multiply -12 × -12 × -12. This operation calculates the value of (-12)^3, resulting in -1,728. 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 2 Step 3: If the calculator has a cube function, press it to calculate (-12)^3. Step 4: If there is no cube function on the calculator, simply multiply -12 three times manually. Step 5: The calculator will display -1,728.

Tips and Tricks for the Cube of -12

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 -12

There are some typical errors that might be made during the process of cubing a number. Let us take a look at five of the major mistakes that might be made:

Problem 1

What is the cube and cube root of -12?

Okay, lets begin

The cube of -12 is -1,728 and the cube root of -12 is approximately -2.289.

Explanation

First, let’s find the cube of -12. 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 (-12)^3 = -1,728 Next, we must find the cube root of -12. 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 ∛(-12) ≈ -2.289 Hence, the cube of -12 is -1,728 and the cube root of -12 is approximately -2.289.

Well explained 👍

Problem 2

If the side length of a cube is -12 cm, what is the volume?

Okay, lets begin

The volume is -1,728 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute -12 for the side length: V = (-12)³ = -1,728 cm³.

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Problem 3

How much smaller is (-12)³ than (-10)³?

Okay, lets begin

(-12)³ - (-10)³ = -728.

Explanation

First find the cube of (-12)³, that is -1,728. Next, find the cube of (-10)³, which is -1,000. Now, find the difference between them using the subtraction method. -1,728 - (-1,000) = -728. Therefore, (-12)³ is -728 smaller than (-10)³.

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Problem 4

If a cube with a side length of -12 cm is compared to a cube with a side length of -6 cm, how much smaller is the volume of the smaller cube?

Okay, lets begin

The volume of the cube with a side length of -12 cm is -1,728 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -12 means multiplying -12 by itself three times: -12 × -12 = 144, and then 144 × -12 = -1,728. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is -1,728 cm³.

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Problem 5

Estimate the cube of -11.9 using the cube of -12.

Okay, lets begin

The cube of -11.9 is approximately -1,728.

Explanation

First, identify the cube of -12, The cube of -12 is (-12)³ = -1,728. Since -11.9 is only a tiny bit more than -12, the cube of -11.9 will be almost the same as the cube of -12. The cube of -11.9 is approximately -1,728 because the difference between -11.9 and -12 is very small. So, we can approximate the value as -1,728.

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FAQs on Cube of -12

1.What is the cube of -12?

The cube of -12 is -1,728.

2.How do you calculate (-12)³?

To calculate (-12)³, use the multiplication method, -12 × -12 × -12, which equals -1,728.

3.What is the meaning of (-12)³?

(-12)³ means -12 multiplied by itself three times, or -12 × -12 × -12.

4.What is the cube root of -12?

The cube root of -12 is approximately -2.289.

5.Is -12 a perfect cube?

No, -12 is not a perfect cube because no integer multiplied by itself three times equals -12.

Important Glossaries for Cube of -12

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, 2^3 represents 2 × 2 × 2 equals 8. Negative Number: A number less than zero, indicated by a minus sign (-), such as -12. Volume: The amount of space occupied by a 3-dimensional object, expressed in cubic units.

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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.