102 LearnersLast updated on May 27th, 2025
Cube of 989
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 989.
Cube of 989
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 989 can be written as 989³, which is the exponential form. Or it can also be written in arithmetic form as 989 × 989 × 989.
How to Calculate the Value of Cube of 989
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 methods help 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. 989³ = 989 × 989 × 989 Step 2: Calculate to get 967,062,209 as the answer. Hence, the cube of 989 is 967,062,209.
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 989 into two parts, as a and b. Let a = 900 and b = 89, so a + b = 989 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term: a³ = 900³ 3a²b = 3 × 900² × 89 3ab² = 3 × 900 × 89² b³ = 89³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (900 + 89)³ = 900³ + 3 × 900² × 89 + 3 × 900 × 89² + 89³ Step 5: Hence, the cube of 989 is 967,062,209.
Using a Calculator
To find the cube of 989 using a calculator, input the number 989 and use the cube function (if available) or multiply 989 × 989 × 989. This operation calculates the value of 989³, resulting in 967,062,209. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 9 followed by 8 and then 9. Step 3: If the calculator has a cube function, press it to calculate 989³. Step 4: If there is no cube function on the calculator, simply multiply 989 three times manually. Step 5: The calculator will display 967,062,209.
Tips and Tricks for the Cube of 989
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 989
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 occur:
Mistake 1
Incorrect Multiplication
One might multiply the numbers only twice. That is, 989 × 989 and not 989 × 989 × 989. Always remember that 989³ = 989 × 989 × 989.
Solved Examples on Cube of 989
Problem 1
What is the cube and cube root of 989?
The cube of 989 is 967,062,209 and the cube root of 989 is approximately 9.973.
Explanation
First, let’s find the cube of 989. We know that the cube of a number, such that x³ = y, where x is the given number, and y is the cubed value of that number. So, we get 989³ = 967,062,209. Next, we must find the cube root of 989. 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 ∛989 ≈ 9.973.
Problem 2
If the side length of the cube is 989 cm, what is the volume?
The volume is 967,062,209 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 989 for the side length: V = 989³ = 967,062,209 cm³.
Problem 3
How much larger is 989³ than 900³?
989³ – 900³ = 706,062,209.
Explanation
First find the cube of 989³, which is 967,062,209. Next, find the cube of 900³, which is 729,000,000. Now, find the difference between them using the subtraction method. 967,062,209 – 729,000,000 = 238,062,209. Therefore, 989³ is 238,062,209 larger than 900³.
Problem 4
If a cube with a side length of 989 cm is compared to a cube with a side length of 500 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 989 cm is 967,062,209 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 989 means multiplying 989 by itself three times: 989 × 989 = 978,121, and then 978,121 × 989 = 967,062,209. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 967,062,209 cm³.
Problem 5
Estimate the cube of 988 using the cube of 989.
The cube of 988 is approximately 967,062,209.
Explanation
First, identify the cube of 989. The cube of 989 is 989³ = 967,062,209. Since 988 is only a tiny bit less than 989, the cube of 988 will be almost the same as the cube of 989. The cube of 988 is approximately 967,062,209 because the difference between 988 and 989 is very small. So, we can approximate the value as 967,062,209.
FAQs on Cube of 989
1.What are the perfect cubes up to 989?
2.How do you calculate 989³?
3.What is the meaning of 989³?
4.What is the cube root of 989?
5.Is 989 a perfect cube?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of 989?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 989?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube of 989
- Binomial Formula: 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: 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 equals 8. - Volume of a Cube: The amount of space occupied by a cube, calculated by raising the side length to the power of three (Side³). - Perfect Cube: A number that is the cube of an integer. For example, 27 is a perfect cube because it is 3³.
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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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