Cube of 3.2

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 3.2 can be written as 3.2³, which is the exponential form. Or it can also be written in arithmetic form as 3.2 × 3.2 × 3.2.

To check whether a number is a cube number or not, we can use the following three methods: 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 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. 3.2³ = 3.2 × 3.2 × 3.2

Step 2: You get approximately 32.768 as the answer. Hence, the cube of 3.2 is approximately 32.768.

The formula for the cube of a binomial (a + b)³ is expanded as a³ + 3a²b + 3ab² + b³.

Step 1: Split the number 3.2 into two parts, such as a = 3 and b = 0.2, so a + b = 3.2.

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

Step 3: Calculate each term: a³ = 3³ 3a²b = 3 × 3² × 0.2 3ab² = 3 × 3 × 0.2² b³ = 0.2³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(3 + 0.2)³ = 3³ + 3 × 3² × 0.2 + 3 × 3 × 0.2² + 0.2³ 3.2³

= 27 + 5.4 + 0.36 + 0.008 3.2³

= 32.768

Step 5: Hence, the cube of 3.2 is approximately 32.768.

To find the cube of 3.2 using a calculator, input the number 3.2 and use the cube function (if available) or multiply 3.2 × 3.2 × 3.2. This operation calculates the value of 3.2³, resulting in approximately 32.768. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 3.2

Step 3: If the calculator has a cube function, press it to calculate 3.2³.

Step 4: If there is no cube function on the calculator, simply multiply 3.2 three times manually.

Step 5: The calculator will display approximately 32.768.

• 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, 3.2³ represents 3.2 × 3.2 × 3.2.

• Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.

• Multiplication Method: A mathematical process used to find the product of numbers or quantities by combining them through repeated addition, often used to compute powers such as squares and cubes.