Cube of 497

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 497 can be written as 497³, which is the exponential form. Or it can also be written in arithmetic form as 497 × 497 × 497.

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 calculate the cubes 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. 497³ = 497 × 497 × 497

Step 2: Calculate the product to get 122,504,873 as the answer.

Hence, the cube of 497 is 122,504,873.

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 497 into two parts, as a and b. Let a = 400 and b = 97, so a + b = 497

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

Step 3: Calculate each term a³ = 400³

3a²b = 3 × 400² × 97

3ab² = 3 × 400 × 97²

b³ = 97³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³

(400 + 97)³ = 400³ + 3 × 400² × 97 + 3 × 400 × 97² + 97³

497³ = 64,000,000 + 46,560,000 + 11,275,200 + 912,673

497³ = 122,504,873

Step 5: Hence, the cube of 497 is 122,504,873.

To find the cube of 497 using a calculator, input the number 497 and use the cube function (if available) or multiply 497 × 497 × 497. This operation calculates the value of 497³, resulting in 122,504,873. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 4 followed by 9 followed by 7

Step 3: If the calculator has a cube function, press it to calculate 497³.

Step 4: If there is no cube function on the calculator, simply multiply 497 three times manually.

Step 5: The calculator will display 122,504,873.

• 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.

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

• Cube Root: The number that when multiplied by itself three times gives the original number.