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Last updated on May 26th, 2025

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Cube of -1

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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 in various mathematical and real-world applications. In this topic, we shall learn about the cube of -1.

Cube of -1 for Vietnamese Students
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Cube of -1

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 -1 can be written as (-1)^3, which is the exponential form. Or it can also be written in arithmetic form as -1 × -1 × -1.

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How to Calculate the Value of Cube of -1

In order to evaluate whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a^3), or by using a calculator. These methods will help individuals to cube numbers efficiently and accurately. By Multiplication Method Using a Formula Using a Calculator

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By Multiplication Method

The multiplication method is a straightforward process in mathematics used to find the product of numbers by multiplying them directly. It's a fundamental operation that helps in understanding more complex mathematical concepts. Step 1: Write down the cube of the given number. (-1)^3 = -1 × -1 × -1 Step 2: You get -1 as the answer. Hence, the cube of -1 is -1.

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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. However, for a single number cube like -1, the formula simplifies to direct multiplication. Step 1: Since the number is -1, set a = -1. Step 2: Calculate a^3 directly: a^3 = (-1)^3 Step 3: The result of (-1) × (-1) × (-1) is -1. Step 4: Hence, the cube of -1 is -1.

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Using a Calculator

To find the cube of -1 using a calculator, input the number -1 and use the cube function (if available) or multiply -1 by itself three times. This operation calculates the value of (-1)^3, resulting in -1. It's a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -1 into the calculator. Step 3: If the calculator has a cube function, use it to calculate (-1)^3. Step 4: If there is no cube function on the calculator, simply multiply -1 three times manually. Step 5: The calculator will display -1.

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Tips and Tricks for the Cube of -1

- The cube of any even number is always even, while the cube of any odd number is always odd. - The cube of a negative number remains negative. - A perfect cube can always be expressed as the product of three identical groups of equal prime factors. - Understanding the sign rules for multiplication can aid in quickly determining the sign of the cube.

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Common Mistakes to Avoid When Calculating the Cube of -1

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

Mistake 1

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Incorrect Multiplication

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Individuals might multiply the numbers only twice. That is, -1 × -1 and not -1 × -1 × -1. Always remember that (-1)^3 = -1 × -1 × -1.

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Solved Examples on Cube of -1

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Problem 1

What is the cube and cube root of -1?

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The cube of -1 is -1, and the cube root of -1 is -1.

Explanation

First, let’s find the cube of -1. We know that the cube of a number is obtained by multiplying the number by itself three times. So, (-1)^3 = -1 × -1 × -1 = -1. Next, we must find the cube root of -1. The cube root of a number is a value that, when cubed, gives the original number. So, the cube root of -1 is -1 because (-1) × (-1) × (-1) = -1.

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Problem 2

If a cube with a side length of -1 cm is imagined, what would be its volume?

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The volume of an imaginary cube with a side length of -1 cm is -1 cm^3.

Explanation

Use the volume formula for a cube V = Side^3. Substitute -1 for the side length: V = (-1)^3 = -1 cm^3.

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Problem 3

Compare the cube of -1 with the cube of 1.

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The cube of -1 is -1, and the cube of 1 is 1.

Explanation

First, find the cube of -1, which is (-1)^3 = -1. Next, find the cube of 1, which is 1^3 = 1. Therefore, the cube of -1 is -1, while the cube of 1 is 1.

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Problem 4

If a cube with a side length of -1 cm is compared to a cube with a side length of 1 cm, what are the volumes?

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The volume of the cube with a side length of -1 cm is -1 cm^3, while the volume of the cube with a side length of 1 cm is 1 cm^3.

Explanation

To find the volume, cube the side lengths: For -1 cm: (-1)^3 = -1 cm^3. For 1 cm: 1^3 = 1 cm^3. Thus, the volume of the cube with -1 cm side is -1 cm^3, and with 1 cm side is 1 cm^3.

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Problem 5

Estimate the cube of -0.9 using the cube of -1.

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The cube of -0.9 is approximately -0.729.

Explanation

First, identify the cube of -1, which is (-1)^3 = -1. Since -0.9 is close to -1, the cube of -0.9 would be slightly more than -1. The exact cube of -0.9 is (-0.9)^3 = -0.729.

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FAQs on Cube of -1

1.What is the cube of -1?

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2.How do you calculate (-1)^3?

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3.What is the meaning of (-1)^3?

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4.What is the cube root of -1?

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5.Is -1 a perfect cube?

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6.How does learning Algebra help students in Vietnam make better decisions in daily life?

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7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of -1?

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8.How do technology and digital tools in Vietnam support learning Algebra and Cube of -1?

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

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Important Glossaries for Cube of -1

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, (-1)^3 represents -1 × -1 × -1. Perfect Cube: A number that can be expressed as the product of an integer with itself three times. Negative Numbers: Numbers less than zero, often resulting in a negative product when multiplied an odd number of times. Cube Root: A value that, when multiplied by itself three times, gives the original number. For example, the cube root of -1 is -1.

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About BrightChamps in Vietnam

At BrightChamps, we believe algebra is more than just numbers—it’s a way to unlock countless chances! We aim to assist children across Vietnam in understanding key math concepts, like today’s focus on the Cube of -1, with a special emphasis on cubes—in a fun, clear, and engaging way. Whether your child is calculating the speed of a roller coaster at Suoi Tien Theme Park, following the scores at a local football match, or managing their allowance to buy the latest gadgets, learning algebra builds their confidence for everyday challenges. Our interactive lessons make math easy and fun. Because kids in Vietnam learn differently, we personalize our teaching to match each child’s style. From Ho Chi Minh City’s lively streets to the beautiful landscapes of Ha Long Bay, BrightChamps brings algebra to life, making it exciting and relevant throughout Vietnam. Let’s make cubes a fun part of every child’s math adventure!
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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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