100 LearnersLast updated on May 27th, 2025
Cube of 849
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 849.
Cube of 849
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 849 can be written as 849³, which is the exponential form. Or it can also be written in arithmetic form as 849 × 849 × 849.
How to Calculate the Value of Cube of 849
In order 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 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 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. 849³ = 849 × 849 × 849 Step 2: Calculate the result. Hence, the cube of 849 is 611,501,649.
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 849 into two parts. Let a = 800 and b = 49, so a + b = 849 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 49 3ab² = 3 × 800 × 49² b³ = 49³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 49)³ = 800³ + 3 × 800² × 49 + 3 × 800 × 49² + 49³ 849³ = 512,000,000 + 94,080,000 + 57,624,000 + 117,649 849³ = 611,501,649 Step 5: Hence, the cube of 849 is 611,501,649.
Using a Calculator
To find the cube of 849 using a calculator, input the number 849 and use the cube function (if available) or multiply 849 × 849 × 849. This operation calculates the value of 849³, resulting in 611,501,649. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 8, 4, and 9. Step 3: If the calculator has a cube function, press it to calculate 849³. Step 4: If there is no cube function on the calculator, simply multiply 849 three times manually. Step 5: The calculator will display 611,501,649.
Tips and Tricks for the Cube of 849
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 849
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, 849 × 849 and not 849 × 849 × 849. Always remember that 849³ = 849 × 849 × 849.
Solved Examples on Cube of 849
Problem 1
What is the cube and cube root of 849?
The cube of 849 is 611,501,649 and the cube root of 849 is approximately 9.454.
Explanation
First, let’s find the cube of 849. We know that the cube of a number is such that x³ = y, where x is the given number, and y is the cubed value of that number. So, we get 849³ = 611,501,649. Next, we must find the cube root of 849. We know that the cube root of a number x is 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√849 ≈ 9.454. Hence, the cube of 849 is 611,501,649 and the cube root of 849 is approximately 9.454.
Problem 2
If the side length of the cube is 849 cm, what is the volume?
The volume is 611,501,649 cm³.
Explanation
Use the volume formula for a cube V = Side³. Substitute 849 for the side length: V = 849³ = 611,501,649 cm³.
Problem 3
How much larger is 849³ than 745³?
849³ – 745³ = 321,362,064.
Explanation
First, find the cube of 849, which is 611,501,649. Next, find the cube of 745, which is 290,139,585. Now, find the difference between them using the subtraction method. 611,501,649 – 290,139,585 = 321,362,064. Therefore, 849³ is 321,362,064 larger than 745³.
Problem 4
If a cube with a side length of 849 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 849 cm is 611,501,649 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 849 means multiplying 849 by itself three times: 849 × 849 = 720,801, and then 720,801 × 849 = 611,501,649. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube. Therefore, the volume of the cube is 611,501,649 cm³.
Problem 5
Estimate the cube of 848.9 using the cube of 849.
The cube of 848.9 is approximately 611,501,649.
Explanation
First, identify the cube of 849, which is 849³ = 611,501,649. Since 848.9 is only a tiny bit less than 849, the cube of 848.9 will be almost the same as the cube of 849. The cube of 848.9 is approximately 611,501,649 because the difference between 848.9 and 849 is very small. So, we can approximate the value as 611,501,649.
FAQs on Cube of 849
1.What is the cube of 849?
2.How do you calculate 849³?
3.What is the meaning of 849³?
4.What is the cube root of 849?
5.Is 849 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 849?
8.How do technology and digital tools in Bahrain support learning Algebra and Cube of 849?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for Cube of 849
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 a cube occupies, calculated as the cube of its side length. Cube Root: A number that, when multiplied by itself three times, gives the original number.
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About BrightChamps in Bahrain
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.
