Cube of 3.1

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 3.1 can be written as 3.1³, which is the exponential form. Or it can also be written in arithmetic form as, 3.1 × 3.1 × 3.1.

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 (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. 3.1³ = 3.1 × 3.1 × 3.1

Step 2: You get approximately 29.791 as the answer. Hence, the cube of 3.1 is approximately 29.791.

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 3.1 into two parts, as 3 and 0.1.

Let a = 3 and b = 0.1,

so a + b = 3.1

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

Step 3: Calculate each term

a³ = 3³

3a²b = 3 × 3² × 0.1

3ab² = 3 × 3 × 0.1²

b³ = 0.1³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³ (3 + 0.1)³

= 3³ + 3 × 3² × 0.1 + 3 × 3 × 0.1² + 0.1³ 3.1³

= 27 + 2.7 + 0.09 + 0.001 3.1³

= approximately 29.791

Step 5: Hence, the cube of 3.1 is approximately 29.791.

To find the cube of 3.1 using a calculator, input the number 3.1 and use the cube function (if available) or multiply 3.1 × 3.1 × 3.1. This operation calculates the value of 3.1³, resulting in approximately 29.791. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 3 followed by .1

Step 3: If the calculator has a cube function, press it to calculate 3.1³.

Step 4: If there is no cube function on the calculator, simply multiply 3.1 three times manually.

Step 5: The calculator will display approximately 29.791.

• 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.

• 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, 2³ represents 2 × 2 × 2 equals 8.

• Decimal Multiplication: The process of multiplying numbers with decimals, ensuring correct placement of decimal points in the result.

• Volume Calculation: The process of determining the space inside a three-dimensional object, calculated by raising the side length of a cube to the power of three.