Cube of 8

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 8 can be written as 8³, which is the exponential form. Or it can also be written in arithmetic form as, 8 × 8 × 8.

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 (a^3), 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. 8³ = 8 × 8 × 8

Step 2: You get 512 as the answer. Hence, the cube of 8 is 512.

The formula (a + b)^3 is a binomial formula for finding the cube of a number. The formula is expanded as a^3 + 3a^2b + 3ab^2 + b^3.

Step 1: Split the number 8 into two parts, as and . Let a = 5 and b = 3, so a + b = 8

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

Step 3: Calculate each term a³ = 5³

3a²b = 3 × 5² × 3

3ab² = 3 × 5 × 3²

b³ = 3³

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

(5 + 3)³ = 5³ + 3 × 5² × 3 + 3 × 5 × 3² + 3³

8³ = 125 + 225 + 135 + 27

8³ = 512

Step 5: Hence, the cube of 8 is 512.

To find the cube of 8 using a calculator, input the number 8 and use the cube function (if available) or multiply 8 × 8 × 8. This operation calculates the value of 8^3, resulting in 512. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 8

Step 3: If the calculator has a cube function, press it to calculate 8³.

Step 4: If there is no cube function on the calculator, simply multiply 8 three times manually.

Step 5: The calculator will display 512.

• 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.

• Perfect Cube: A number that can be expressed as an integer multiplied by itself three times.

• 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, 8³ represents 8 × 8 × 8 equals 512.

• Volume Formula for a Cube: The volume of a cube is calculated as the cube of its side length, expressed as V = Side³.