Cube of 1002

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 1002 can be written as 1002³, which is the exponential form. Or it can also be written in arithmetic form as, 1002 × 1002 × 1002.

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 students 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. 1002³ = 1002 × 1002 × 1002

Step 2: You get 1,008,024,008 as the answer. Hence, the cube of 1002 is 1,008,024,008.

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 1002 into two parts, as 1000 and 2. Let a = 1000 and b = 2, so a + b = 1002

Step 2: Now, apply the formula (a+b)³ = a³ + 3a²b + 3ab² + b³

Step 3: Calculate each term

a³ = 1000³

3a²b = 3 × 1000² × 2

3ab² = 3 × 1000 × 2²

b³ = 2³

Step 4: Add all the terms together:

(a+b)³ = a³ + 3a²b + 3ab² + b³

(1000+2)³ = 1000³ + 3 × 1000² × 2 + 3 × 1000 × 2² + 2³

1002³ = 1,000,000,000 + 6,000,000 + 12,000 + 8

1002³ = 1,008,024,008

Step 5: Hence, the cube of 1002 is 1,008,024,008.

To find the cube of 1002 using a calculator, input the number 1002 and use the cube function (if available) or multiply 1002 × 1002 × 1002. This operation calculates the value of 1002³, resulting in 1,008,024,008. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1 followed by 0, 0, and 2.

Step 3: If the calculator has a cube function, press it to calculate 1002³.

Step 4: If there is no cube function on the calculator, simply multiply 1002 three times manually.

Step 5: The calculator will display 1,008,024,008.

• 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 sum, 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. For example, 2³ represents 2 × 2 × 2 equals 8.

• Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice more (e.g., 8 is a perfect cube because it is 2 × 2 × 2).

• Cube Root: The inverse operation of cubing, which finds the number that, when cubed, equals the original number. The cube root of x is written as ∛x.