100 LearnersLast updated on May 27th, 2025
Cube of 982
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 cubes of 982.
Cube of 982
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 by itself three times results in a negative number. The cube of 982 can be written as 982³, which is the exponential form. Or it can also be written in arithmetic form as, 982 × 982 × 982.
How to Calculate the Value of Cube of 982
In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These three methods will help learners 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. 982³ = 982 × 982 × 982 Step 2: Calculate the result. You get 946,932,088 as the answer. Hence, the cube of 982 is 946,932,088.
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 982 into two parts. Let a = 980 and b = 2, so a + b = 982 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term: a³ = 980³ 3a²b = 3 × 980² × 2 3ab² = 3 × 980 × 2² b³ = 2³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (980 + 2)³ = 980³ + 3 × 980² × 2 + 3 × 980 × 2² + 2³ 982³ = 941,192,000 + 5,760 + 11,520 + 8 982³ = 946,932,088 Step 5: Hence, the cube of 982 is 946,932,088.
Using a Calculator
To find the cube of 982 using a calculator, input the number 982 and use the cube function (if available) or multiply 982 × 982 × 982. This operation calculates the value of 982³, resulting in 946,932,088. 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 2. Step 3: If the calculator has a cube function, press it to calculate 982³. Step 4: If there is no cube function on the calculator, simply multiply 982 three times manually. Step 5: The calculator will display 946,932,088.
Tips and Tricks for the Cube of 982
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 982
There are some typical errors that learners might make during the process of cubing a number. Let us take a look at five of the major mistakes that learners might make:
Mistake 1
Incorrect Multiplication
Learners might multiply the numbers only twice. That is, 982 × 982 and not 982 × 982 × 982. Always remember that 982³ = 982 × 982 × 982.
Solved Examples on Cube of 982
Problem 1
What is the cube and cube root of 982?
The cube of 982 is 946,932,088 and the cube root of 982 is approximately 9.956.
Explanation
First, let’s find the cube of 982. 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 982³ = 946,932,088 Next, we must find the cube root of 982. We know that the cube root of a number ‘x’, such that ³√x = y Where x is the given number, and y is the cube root value of the number So, we get ³√982 ≈ 9.956 Hence the cube of 982 is 946,932,088 and the cube root of 982 is approximately 9.956.
Problem 2
If the side length of the cube is 982 cm, what is the volume?
The volume is 946,932,088 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 982 for the side length: V = 982³ = 946,932,088 cm³.
Problem 3
How much larger is 982³ than 980³?
982³ – 980³ = 5,776.
Explanation
First find the cube of 982, which is 946,932,088. Next, find the cube of 980, which is 941,192,000. Now, find the difference between them using the subtraction method. 946,932,088 – 941,192,000 = 5,776 Therefore, 982³ is 5,776 larger than 980³.
Problem 4
If a cube with a side length of 982 cm is compared to a cube with a side length of 2 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 982 cm is 946,932,088 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 982 means multiplying 982 by itself three times: 982 × 982 = 964,324, and then 964,324 × 982 = 946,932,088. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 946,932,088 cm³.
Problem 5
Estimate the cube of 981.5 using the cube of 982.
The cube of 981.5 is approximately 946,932,088.
Explanation
First, identify the cube of 982. The cube of 982 is 982³ = 946,932,088. Since 981.5 is only a tiny bit less than 982, the cube of 981.5 will be almost the same as the cube of 982. The cube of 981.5 is approximately 946,932,088 because the difference between 981.5 and 982 is very small. So, we can approximate the value as 946,932,088.
FAQs on Cube of 982
1.What are the perfect cubes up to 982?
2.How do you calculate 982³?
3.What is the meaning of 982³?
4.What is the cube root of 982?
5.Is 982 a perfect cube?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 982?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 982?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 982
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 equals 8. Multiplication Method: This is a method to find the cube by multiplying the base number by itself three times. Perfect Cube: A number that can be expressed as the product of three identical integers.
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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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