Cube of 275

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 275 can be written as 275³, which is the exponential form.

Or it can also be written in arithmetic form as 275 × 275 × 275.

To determine whether a number is a cube number, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These methods will help calculate cubes faster and easier without confusion or being stuck while evaluating the answers.

• By Multiplication Method
   
• Using a Formula
   
• 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. 275³ = 275 × 275 × 275

Step 2: Calculate the result, which is 20,796,875. Hence, the cube of 275 is 20,796,875.

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 275 into two parts, such as a = 270 and b = 5, so a + b = 275.

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

Step 3: Calculate each term: a³ = 270³ 3a²b = 3 × 270² × 5 3ab² = 3 × 270 × 5² b³ = 5³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (270 + 5)³ = 270³ + 3 × 270² × 5 + 3 × 270 × 5² + 5³ 275³ = 19,683,000 + 109,350 + 20,250 + 125 275³ = 20,796,875

Step 5: Hence, the cube of 275 is 20,796,875.

To find the cube of 275 using a calculator, input the number 275 and use the cube function (if available) or multiply 275 × 275 × 275. This operation calculates the value of 275³, resulting in 20,796,875. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 2 followed by 7 and 5.

Step 3: If the calculator has a cube function, press it to calculate 275³.

Step 4: If there is no cube function on the calculator, simply multiply 275 three times manually.

Step 5: The calculator will display 20,796,875.

• 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 is the cube of an integer.
   
• Cube Root: The number that produces a given number when cubed, denoted as ∛x.