Cube of 19

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 19 can be written as 19³, which is the exponential form. Or it can also be written in arithmetic form as, 19 × 19 × 19.

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 kids 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. 19³ = 19 × 19 × 19

Step 2: You get 6,859 as the answer. Hence, the cube of 19 is 6,859.

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 19 into two parts, such as 10 and 9. Let a = 10 and b = 9, so a + b = 19.

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

Step 3: Calculate each term

a³ = 10³

3a²b = 3 × 10² × 9

3ab² = 3 × 10 × 9²

b³ = 9³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(10 + 9)³ = 10³ + 3 × 10² × 9 + 3 × 10 × 9² + 9³

19³ = 1,000 + 2,700 + 2,430 + 729 19³ = 6,859

Step 5: Hence, the cube of 19 is 6,859.

To find the cube of 19 using a calculator, input the number 19 and use the cube function (if available) or multiply 19 × 19 × 19. This operation calculates the value of 19³, resulting in 6,859. 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.

Step 3: If the calculator has a cube function, press it to calculate 19³.

Step 4: If there is no cube function on the calculator, simply multiply 19 three times manually.

Step 5: The calculator will display 6,859.

• 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.

• Cube Root: The cube root of a number is a value that, when multiplied by itself twice, gives the original number. It is represented as ∛x.

• Volume of a Cube: The space inside a cube, calculated as the cube of the side length, given by V = Side³.