Cube of 4.25

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 4.25 can be written as 4.25³, which is the exponential form. Or it can also be written in arithmetic form as, 4.25 × 4.25 × 4.25.

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 you 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 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. 4.25³ = 4.25 × 4.25 × 4.25

Step 2: You get approximately 76.765625 as the answer. Hence, the cube of 4.25 is approximately 76.765625.

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 4.25 into two parts, as 4 and 0.25. Let a = 4 and b = 0.25, so a + b = 4.25

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

Step 3: Calculate each term a³ = 4³ 3a²b = 3 × 4² × 0.25 3ab² = 3 × 4 × 0.25² b³ = 0.25³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(4 + 0.25)³ = 4³ + 3 × 4² × 0.25 + 3 × 4 × 0.25² + 0.25³

4.25³ = 64 + 12 + 0.75 + 0.015625

4.25³ = 76.765625

Step 5: Hence, the cube of 4.25 is approximately 76.765625.

To find the cube of 4.25 using a calculator, input the number 4.25 and use the cube function (if available) or multiply 4.25 × 4.25 × 4.25. This operation calculates the value of 4.25³, resulting in approximately 76.765625. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 4.25

Step 3: If the calculator has a cube function, press it to calculate 4.25³.

Step 4: If there is no cube function on the calculator, simply multiply 4.25 three times manually.

Step 5: The calculator will display approximately 76.765625.

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.

• Cube Root: A number that, when multiplied by itself twice, gives the original number. For instance, the cube root of 27 is 3.

• Multiplication Method: A mathematical technique used to find the product of numbers by combining them through repeated addition.