Cube of 103

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 103 can be written as 103³, which is the exponential form.

Or it can also be written in arithmetic form as 103 × 103 × 103.

In order to determine 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 to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

• By Multiplication Method
   
• Using a Formula (a³)
   
• 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. 103³ = 103 × 103 × 103

Step 2: You get 1,092,727 as the answer.

Hence, the cube of 103 is 1,092,727.

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 103 into two parts. Let a = 100 and b = 3, so a + b = 103.

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

Step 3: Calculate each term. a³ = 100³ 3a²b = 3 × 100² × 3 3ab² = 3 × 100 × 3² b³ = 3³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 3)³ = 100³ + 3 × 100² × 3 + 3 × 100 × 3² + 3³ 103³ = 1,000,000 + 90,000 + 2,700 + 27 103³ = 1,092,727

Step 5: Hence, the cube of 103 is 1,092,727.

To find the cube of 103 using a calculator, input the number 103 and use the cube function (if available) or multiply 103 × 103 × 103. This operation calculates the value of 103³, resulting in 1,092,727. 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, then 3.

Step 3: If the calculator has a cube function, press it to calculate 103³.

Step 4: If there is no cube function on the calculator, simply multiply 103 three times manually.

Step 5: The calculator will display 1,092,727.

• 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.

• Perfect Cube: A number that can be expressed as the cube of an integer.

• Volume: The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great. For cubes, it is calculated as side³.