Cube of 1097

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 multiplying a negative number by itself three times results in a negative number. The cube of 1097 can be written as 1097³, which is the exponential form. Or it can also be written in arithmetic form as, 1097 × 1097 × 1097.

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (\(a^3\)), or by using a calculator. These three methods will help students to cube the numbers faster and easier without feeling confused or 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. 1097³ = 1097 × 1097 × 1097

Step 2: Calculate the result. The cube of 1097 is 1,320,058,273.

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 1097 into two parts. Let a = 1000 and b = 97, so a + b = 1097.

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

Step 3: Calculate each term: a³ = 1000³ 

3a²b = 3 × 1000² × 97

3ab² = 3 × 1000 × 97²

b³ = 97³

Step 4: Add all the terms together: (1000 + 97)³ = 1000³ + 3 × 1000² × 97 + 3 × 1000 × 97² + 97³

1097³ = 1,000,000,000 + 291,000,000 + 28,233,000 + 912,673

1097³ = 1,320,058,273

Step 5: Hence, the cube of 1097 is 1,320,058,273.

To find the cube of 1097 using a calculator, input the number 1097 and use the cube function (if available) or multiply 1097 × 1097 × 1097. This operation calculates the value of \(1097^3\), resulting in 1,320,058,273. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 1097. Step 3: If the calculator has a cube function, press it to calculate \(1097^3\). Step 4: If there is no cube function on the calculator, simply multiply 1097 three times manually. Step 5: The calculator will display 1,320,058,273.

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 indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2, which equals 8.

• Cube Root: The number which when multiplied by itself three times gives the original number. For example, the cube root of 27 is 3 because 3³ = 27.

• Perfect Cube: A number that can be expressed as the cube of an integer. Examples include 1, 8, 27, 64, etc.