101 LearnersLast updated on May 27th, 2025
Cube of 991
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 991.
Cube of 991
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 991 can be written as 991³, which is the exponential form. Or it can also be written in arithmetic form as 991 × 991 × 991.
How to Calculate the Value of Cube of 991
In order to check whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids 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. It is a fundamental operation that forms the basis for more complex mathematical concepts. Step 1: Write down the cube of the given number. 991³ = 991 × 991 × 991 Step 2: You get 973,764,271 as the answer. Hence, the cube of 991 is 973,764,271.
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 991 into two parts, as 900 and 91. Let a = 900 and b = 91, so a + b = 991 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³= 900³ 3a²b = 3 × 900² × 91 3ab² = 3 × 900 × 91² b³ = 91³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (900 + 91)³ = 900³ + 3 × 900² × 91 + 3 × 900 × 91² + 91³ 991³ = 729,000,000 + 220,410,000 + 22,292,700 + 753,571 991³ = 973,764,271 Step 5: Hence, the cube of 991 is 973,764,271.
Using a Calculator
To find the cube of 991 using a calculator, input the number 991 and use the cube function (if available) or multiply 991 × 991 × 991. This operation calculates the value of 991³, resulting in 973,764,271. 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 9 and 1 Step 3: If the calculator has a cube function, press it to calculate 991³. Step 4: If there is no cube function on the calculator, simply multiply 991 three times manually. Step 5: The calculator will display 973,764,271.
Tips and Tricks for the Cube of 991
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 991
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, 991 × 991 and not 991 × 991 × 991. Always remember that 991³ = 991 × 991 × 991.
Solved Examples on Cube of 991
Problem 1
What is the cube and cube root of 991?
The cube of 991 is 973,764,271 and the cube root of 991 is approximately 9.97.
Explanation
First, let’s find the cube of 991. 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 991³ = 973,764,271 Next, we must find the cube root of 991 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√991 ≈ 9.97 Hence, the cube of 991 is 973,764,271 and the cube root of 991 is approximately 9.97.
Problem 2
If the side length of the cube is 991 cm, what is the volume?
The volume is 973,764,271 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 991 for the side length: V = 991³ = 973,764,271 cm³.
Problem 3
How much larger is 991³ than 900³?
991³ – 900³ = 244,764,271.
Explanation
First, find the cube of 991³, that is 973,764,271 Next, find the cube of 900³, which is 729,000,000 Now, find the difference between them using the subtraction method. 973,764,271 – 729,000,000 = 244,764,271 Therefore, 991³ is 244,764,271 larger than 900³.
Problem 4
If a cube with a side length of 991 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 991 cm is 973,764,271 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 991 means multiplying 991 by itself three times: 991 × 991 = 982,081, and then 982,081 × 991 = 973,764,271. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is 973,764,271 cm³.
Problem 5
Estimate the cube 990.9 using the cube 991.
The cube of 990.9 is approximately 973,764,271.
Explanation
First, identify the cube of 991, The cube of 991 is 991³ = 973,764,271. Since 990.9 is only a tiny bit less than 991, the cube of 990.9 will be almost the same as the cube of 991. The cube of 990.9 is approximately 973,764,271 because the difference between 990.9 and 991 is very small. So, we can approximate the value as 973,764,271.
FAQs on Cube of 991
1.What are the perfect cubes up to 991?
2.How do you calculate 991³?
3.What is the meaning of 991³?
4.What is the cube root of 991?
5.Is 991 a perfect cube?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Cube of 991?
8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 991?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for Cube of 991
Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer. 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. Perfect Cube: A number that can be expressed as the cube of an integer, such as 1, 8, 27, etc. Volume of a Cube: The amount of space inside a cube, calculated as the cube of the side length.
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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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: He loves to play the quiz with kids through algebra to make kids love it.
