Cube of 198

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 198 can be written as 198³, which is the exponential form. Or it can also be written in arithmetic form as 198 × 198 × 198.

To determine whether a number is a cube number, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help find the cube of numbers faster and easier without confusion during evaluation.

• By Multiplication Method
• Using a Formula
• Using a Calculator

The multiplication method is a process in mathematics used to find the product of 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. 198³ = 198 × 198 × 198

Step 2: You get 7,774,872 as the answer.

Hence, the cube of 198 is 7,774,872.

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 198 into two parts.

Let a = 200 and b = -2, so a + b = 198

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

Step 3: Calculate each term a³ = 200³ , 3a²b = 3 × 200² × (-2) , 3ab² = 3 × 200 × (-2)²  , b³ = (-2)³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³

(200 - 2)³ = 200³ + 3 × 200² × (-2) + 3 × 200 × (-2)² + (-2)³ 198³

= 8,000,000 - 240,000 + 2,400 - 8 198³ = 7,774,872

Step 5: Hence, the cube of 198 is 7,774,872.

To find the cube of 198 using a calculator, input the number 198 and use the cube function (if available) or multiply 198 × 198 × 198. This operation calculates the value of 198³, resulting in 7,774,872. 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 9, and then 8.

Step 3: If the calculator has a cube function, press it to calculate 198³.

Step 4: If there is no cube function on the calculator, simply multiply 198 three times manually.

Step 5: The calculator will display 7,774,872.

• 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, which equals 8.
  
   
• Perfect Cube: A number that can be expressed as the cube of an integer.
  
   
• Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.