Cube of 678

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 678 can be written as 678³, which is the exponential form. Or it can also be written in arithmetic form as 678 × 678 × 678.

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. 678³ = 678 × 678 × 678

Step 2: You get 311,213,352 as the answer. Hence, the cube of 678 is 311,213,352.

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 678 into two parts. Let a = 600 and b = 78, so a + b = 678

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

Step 3: Calculate each term

a³ = 600³

3a²b = 3 × 600² × 78

3ab² = 3 × 600 × 78²

b³ = 78³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(600 + 78)³ = 600³ + 3 × 600² × 78 + 3 × 600 × 78² + 78³

678³ = 216,000,000 + 84,240,000 + 10,953,600 + 474,552

678³ = 311,213,352

Step 5: Hence, the cube of 678 is 311,213,352.

To find the cube of 678 using a calculator, input the number 678 and use the cube function (if available) or multiply 678 × 678 × 678. This operation calculates the value of 678³, resulting in 311,213,352. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 6 followed by 7 and 8

Step 3: If the calculator has a cube function, press it to calculate 678³.

Step 4: If there is no cube function on the calculator, simply multiply 678 three times manually.

Step 5: The calculator will display 311,213,352.

• 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 product of an integer multiplied by itself twice more.

• Cube Root: The number that, when multiplied by itself three times, gives the original number, denoted by the symbol ∛.