Cube of 784

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 784 can be written as 784³, which is the exponential form. Or it can also be written in arithmetic form as 784 × 784 × 784.

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. -

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. 784³ = 784 × 784 × 784

Step 2: You get 482,285,184 as the answer. Hence, the cube of 784 is 482,285,184.

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 784 into two parts, as 700 and 84. Let a = 700 and b = 84, so a + b = 784

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

Step 3: Calculate each term

a³= 700³

3a²b = 3 × 700² × 84

3ab² = 3 × 700 × 84²

b³ = 84³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(700 + 84)³ = 700³ + 3 × 700² × 84 + 3 × 700 × 84² + 84³

784³ = 343,000,000 + 123,480,000 + 14,779,200 + 592,984

784³ = 482,285,184

Step 5: Hence, the cube of 784 is 482,285,184.

To find the cube of 784 using a calculator, input the number 784 and use the cube function (if available) or multiply 784 × 784 × 784. This operation calculates the value of 784³, resulting in 482,285,184. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 7, 8, and 4 sequentially.

Step 3: If the calculator has a cube function, press it to calculate 784³.

Step 4: If there is no cube function on the calculator, simply multiply 784 three times manually.

Step 5: The calculator will display 482,285,184.

• 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 sum, 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. 

• Multiplication Method: A process in mathematics used to find the product of numbers by combining them through repeated addition. 

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