Cube of 1328

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 1328 can be written as \(1328^3\), which is the exponential form. Or it can also be written in arithmetic form as, 1328 × 1328 × 1328.

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. 1328³ = 1328 × 1328 × 1328

Step 2: Calculate the final product. Hence, the cube of 1328 is 2,342,974,592.

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 1328 into two parts, as 1300 and 28. Let a = 1300 and b = 28, so a + b = 1328.

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

Step 3: Calculate each term: (a³ = 1300³)

3a²b = 3 × 1300² × 28

3ab² = 3 × 1300 × 28²

b³ = 28³

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

(1300 + 28)³ = 1300³ + 3 × 1300² × 28 + 3 × 1300 × 28² + 28³

1328³ = 2,197,000,000 + 1,416,000 + 30,744 + 21,952

1328³ = 2,342,974,592

Step 5: Hence, the cube of 1328 is 2,342,974,592.

To find the cube of 1328 using a calculator, input the number 1328 and use the cube function (if available) or multiply 1328 × 1328 × 1328. This operation calculates the value of 1328³, resulting in 2,342,974,592. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 1328.

Step 3: If the calculator has a cube function, press it to calculate 1328³.

Step 4: If there is no cube function on the calculator, simply multiply 1328 three times manually.

Step 5: The calculator will display 2,342,974,592.

• 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 equals 8.

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

• Cube Root: The number that produces a given number when cubed. For example, the cube root of 8 is 2, since 2³ = 8.