Cube of 120

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 120 can be written as 120³, which is the exponential form.

Or it can also be written in arithmetic form as 120 × 120 × 120.

In order to check whether a number is a cube number or not, we can use the following three methods, such as 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
   
• 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. 120³ = 120 × 120 × 120

Step 2: You get 1,728,000 as the answer. Hence, the cube of 120 is 1,728,000.

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 120 into two parts. Let a = 100 and b = 20, so a + b = 120

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

Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 20 3ab² = 3 × 100 × 20² b³ = 20³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 20)³ = 100³ + 3 × 100² × 20 + 3 × 100 × 20² + 20³ 120³ = 1,000,000 + 600,000 + 120,000 + 8,000 120³ = 1,728,000

Step 5: Hence, the cube of 120 is 1,728,000.

To find the cube of 120 using a calculator, input the number 120 and use the cube function (if available) or multiply 120 × 120 × 120. This operation calculates the value of 120³, resulting in 1,728,000. 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 2 and 0

Step 3: If the calculator has a cube function, press it to calculate 120³.

Step 4: If there is no cube function on the calculator, simply multiply 120 three times manually.

Step 5: The calculator will display 1,728,000.

• 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: It is 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: It is 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 occupied by a 3-dimensional object, often measured in cubic units.