Cube of 189

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 189 can be written as (189³), which is the exponential form. Or it can also be written in arithmetic form as, 189 × 189 × 189.

In order to check whether a number is a cube number or not, we can use the following three methods, such as 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. (189³ = 189)

Step 2: You get 6,737,829 as the answer.

Hence, the cube of 189 is 6,737,829.

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 189 into two parts. Let (a = 180) and (b = 9), so (a + b = 189).

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

Step 3: Calculate each term: (a³= 180³) 

(3a²b = 3 × 180² × 9)

(3ab²= 3 × 180× 9²)

(b³ = 9³)

Step 4: Add all the terms together: ((a + b)³ = a³ + 3a²b + 3ab² + b³) ((180 + 9)³ = 180³ + 3 ×180² × 9 + 3 ×180 × 9² + 9³)

(189³= 5,832,000 + 874,800 + 43,740 + 729)

(189³ = 6,737,829)

Step 5: Hence, the cube of 189 is 6,737,829.

To find the cube of 189 using a calculator, input the number 189 and use the cube function (if available) or multiply 189 × 189 × 189. This operation calculates the value of (189³), resulting in 6,737,829. 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 8 and 9.

Step 3: If the calculator has a cube function, press it to calculate (189³).

Step 4: If there is no cube function on the calculator, simply multiply 189 three times manually.

Step 5: The calculator will display 6,737,829.

• 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.
  
   
• Volume of a Cube: The space inside a cube, calculated by raising the side length to the power of three.
  
   
• Perfect Cube: A number that can be expressed as the cube of an integer.