123 LearnersLast updated on May 26th, 2025
Cube of -2
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 -2.
Cube of -2
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 -2 can be written as (-2)³, which is the exponential form. Or it can also be written in arithmetic form as, -2 × -2 × -2.
How to Calculate the Value of Cube of -2
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 students to cube 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 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. (-2)³ = -2 × -2 × -2 Step 2: Multiply the numbers step-by-step. First, -2 × -2 = 4. Then, 4 × -2 = -8. Hence, the cube of -2 is -8.
Using a Formula (a³)
The formula for cubing a number is a³, where 'a' is the number. For the number -2, the cube is calculated directly as follows: Step 1: Apply the formula a³ to the number -2. (-2)³ = -2 × -2 × -2 Step 2: Calculate the result. -2 × -2 = 4 4 × -2 = -8 Step 3: Therefore, the cube of -2 is -8.
Using a Calculator
To find the cube of -2 using a calculator, input the number -2 and use the cube function (if available) or multiply -2 × -2 × -2. This operation calculates the value of (-2)³, resulting in -8. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -2 into the calculator. Step 3: If the calculator has a cube function, press it to calculate (-2)³. Step 4: If there is no cube function on the calculator, simply multiply -2 three times manually. Step 5: The calculator will display -8.
Tips and Tricks for the Cube of -2
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 -2
There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:
Mistake 1
Incorrect Multiplication
Students might multiply the numbers only twice. That is, -2 × -2 and not -2 × -2 × -2. Always remember that (-2)³ = -2 × -2 × -2.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility that students 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
Calculator Misuse
Students 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
Misplacing Negative Signs
Misplacing negative signs during manual multiplication leads to incorrect results like 8 instead of -8. For this, students should always double-check their answers.
Mistake 5
Assuming Negative Cubes are Positive
Students might incorrectly assume that cubing a negative number results in a positive number. In order to avoid this, remember that the cube of a negative number is always negative.
Solved Examples on Cube of -2
Problem 1
What is the cube and cube root of -2?
The cube of -2 is -8 and the cube root of -2 is approximately -1.26.
Explanation
First, let’s find the cube of -2. We know that the cube of a number is x³ = y, where x is the given number, and y is the cubed value of that number. So, we get (-2)³ = -8. Next, we must find the cube root of -2. We know that the cube root of a number 'x' is such that ∛x = y, where 'x' is the given number, and y is the cube root value of the number. So, we get ∛(-2) ≈ -1.26. Hence the cube of -2 is -8 and the cube root of -2 is approximately -1.26.
Problem 2
If the side length of a cube is -2 cm, what is the volume?
The volume is -8 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute -2 for the side length: V = (-2)³ = -8 cm³.
Problem 3
How much larger is (-2)³ than 1³?
(-2)³ - 1³ = -9.
Explanation
First find the cube of (-2)³, which is -8. Next, find the cube of 1³, which is 1. Now, find the difference between them using the subtraction method. -8 - 1 = -9. Therefore, (-2)³ is -9 less than 1³.
Problem 4
If a cube with a side length of -2 cm is compared to a cube with a side length of 2 cm, how much smaller is the volume of the smaller cube?
The volume of the cube with a side length of -2 cm is -8 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -2 means multiplying -2 by itself three times: -2 × -2 = 4, and then 4 × -2 = -8. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is -8 cm³.
Problem 5
Estimate the cube of -1.9 using the cube of -2.
The cube of -1.9 is approximately -6.86.
Explanation
First, identify the cube of -2, The cube of -2 is (-2)³ = -8. Since -1.9 is slightly greater than -2, the cube of -1.9 will be slightly greater than the cube of -2. The cube of -1.9 is approximately -6.86 because it is closer to -2. So, we can estimate the value as approximately -6.86.
FAQs on Cube of -2
1.What are the perfect cubes up to -2?
2.How do you calculate (-2)³?
3.What is the meaning of (-2)³?
4.What is the cube root of -2?
5.Is -2 a perfect cube?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Cube of -2?
8.How do technology and digital tools in India support learning Algebra and Cube of -2?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Cube of -2
- 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, where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2, which equals 8. - Negative Number: A number less than zero, often indicated by a minus sign (-). - Perfect Cube: A number that is the cube of an integer. - Cube Root: The 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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Jaskaran Singh Saluja
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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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