102 LearnersLast updated on May 26th, 2025
Cube of -20
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 -20.
Cube of -20
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 -20 can be written as (-20)³, which is the exponential form. Or it can also be written in arithmetic form as -20 × -20 × -20.
How to Calculate the Value of the Cube of -20
To determine whether a number is a cube number, 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. - 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, which is a fundamental operation that forms the basis for more complex mathematical concepts. Step 1: Write down the cube of the given number. (-20)³ = -20 × -20 × -20 Step 2: You get -8,000 as the answer. Hence, the cube of -20 is -8,000.
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 -20 into two parts. Let a = -10 and b = -10, so a + b = -20 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = (-10)³ 3a²b = 3 × (-10)² × (-10) 3ab² = 3 × (-10) × (-10)² b³ = (-10)³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (-10 + -10)³ = (-10)³ + 3 × (-10)² × (-10) + 3 × (-10) × (-10)² + (-10)³ (-20)³ = -1,000 - 3,000 - 3,000 - 1,000 (-20)³ = -8,000 Step 5: Hence, the cube of -20 is -8,000.
Using a Calculator
To find the cube of -20 using a calculator, input the number -20 and use the cube function (if available) or multiply -20 × -20 × -20. This operation calculates the value of (-20)³, resulting in -8,000. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press -2 followed by 0 Step 3: If the calculator has a cube function, press it to calculate (-20)³. Step 4: If there is no cube function on the calculator, simply multiply -20 three times manually. Step 5: The calculator will display -8,000.
Tips and Tricks for the Cube of -20
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 -20
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
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, -20 × -20 and not -20 × -20 × -20. Always remember that (-20)³ = -20 × -20 × -20.
Solved Examples on Cube of -20
Problem 1
What is the cube and cube root of -20?
The cube of -20 is -8,000 and the cube root of -20 is approximately -2.714.
Explanation
First, let’s find the cube of -20. We know that the cube of a number is calculated by raising it to the power of 3, such that x³ = y. So, we get (-20)³ = -8,000. Next, we must find the cube root of -20. We know that the cube root of a number ‘x’ is such that ∛x = y. So, we get ∛(-20) ≈ -2.714. Hence, the cube of -20 is -8,000 and the cube root of -20 is approximately -2.714.
Problem 2
If the side length of a cube is -20 cm, what is the volume?
The volume is -8,000 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute -20 for the side length: V = (-20)³ = -8,000 cm³.
Problem 3
How much larger is 10³ than (-20)³?
10³ - (-20)³ = 9,900.
Explanation
First, find the cube of 10, which is 1,000. Next, find the cube of -20, which is -8,000. Now, find the difference between them using the subtraction method. 1,000 - (-8,000) = 9,000 + 1,000 = 9,900. Therefore, 10³ is 9,900 larger than (-20)³.
Problem 4
If a cube with a side length of 10 cm is compared to a cube with a side length of -20 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 10 cm is 1,000 cm³.
Explanation
To find its 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), because we are calculating the space inside the cube. Therefore, the volume of the cube is 1,000 cm³.
Problem 5
Estimate the cube of -19.9 using the cube of -20.
The cube of -19.9 is approximately -7,880.
Explanation
First, identify the cube of -20, The cube of -20 is (-20)³ = -8,000. Since -19.9 is slightly more than -20, the cube of -19.9 will be slightly more than the cube of -20. The cube of -19.9 is approximately -7,880 because the difference between -19.9 and -20 is very small. So, we can approximate the value as -7,880.
FAQs on Cube of -20
1.What are the perfect cubes up to 20?
2.How do you calculate (-20)³?
3.What is the meaning of (-20)³?
4.What is the cube root of -20?
5.Is -20 a perfect cube?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Cube of -20?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube of -20?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for Cube of -20
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, which equals 8. Negative Number Cubing: When a negative number is cubed, the result is negative because the product of three negative factors is negative. Volume Formula for Cube: The formula to calculate the volume of a cube is Side³, where the side is the length of any edge of the cube.
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About BrightChamps in United Arab Emirates
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.
