Cube of 3.75

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 3.75 can be written as 3.75³, which is the exponential form. Or it can also be written in arithmetic form as, 3.75 × 3.75 × 3.75.

In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube 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. 3.75³ = 3.75 × 3.75 × 3.75

Step 2: You get approximately 52.734375 as the answer. Hence, the cube of 3.75 is approximately 52.734375.

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 3.75 into two parts, as 3 and 0.75. Let a = 3 and b = 0.75, so a + b = 3.75

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

Step 3: Calculate each term

a³ = 3³

3a²b = 3 × 3² × 0.75

3ab² = 3 × 3 × 0.75²

b³ = 0.75³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(3 + 0.75)³ = 3³ + 3 × 3² × 0.75 + 3 × 3 × 0.75² + 0.75³ 3.75³

= 27 + 20.25 + 5.0625 + 0.421875 3.75³

= 52.734375

Step 5: Hence, the cube of 3.75 is approximately 52.734375.

To find the cube of 3.75 using a calculator, input the number 3.75 and use the cube function (if available) or multiply 3.75 × 3.75 × 3.75. This operation calculates the value of 3.75³, resulting in approximately 52.734375. 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 .75

Step 3: If the calculator has a cube function, press it to calculate 3.75³.

Step 4: If there is no cube function on the calculator, simply multiply 3.75 three times manually.

Step 5: The calculator will display approximately 52.734375.

• The cube of any positive number is always positive, while the cube of any negative number is always negative.

• 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 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, 3⁴ represents 3 × 3 × 3 × 3 equals 81.

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

• Cube Root: A number that produces a specified quantity when multiplied by itself twice. For example, the cube root of 27 is 3 because 3 × 3 × 3 equals 27.