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.

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.

1. By Multiplication Method
2. Using a Formula
3. Using a Calculator

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.

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.

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.

• 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.

• 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.