Cube of 517

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 517 can be written as 517³, which is the exponential form. Or it can also be written in arithmetic form as, 517 × 517 × 517.

To calculate whether a number is a cube number, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These methods help calculate the cube of numbers more efficiently without feeling confused or stuck.

• By Multiplication Method
   
• Using a Formula
   
• 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 multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number.

517³ = 517 × 517 × 517

Step 2: You get 137,078,213 as the answer.

Hence, the cube of 517 is 137,078,213.

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 517 into two parts.

Let a = 500 and b = 17, so a + b = 517

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

Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 17 , 3ab² = 3 × 500 × 17² , b³ = 17³

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

(500 + 17)³ = 500³ + 3 × 500² × 17 + 3 × 500 × 17² + 17³ 517³

= 125,000,000 + 12,750,000 + 433,500 + 4,913 517³

= 137,078,213

Step 5: Hence, the cube of 517 is 137,078,213.

To find the cube of 517 using a calculator, input the number 517 and use the cube function (if available) or multiply 517 × 517 × 517. This operation calculates the value of 517³, resulting in 137,078,213. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 517

Step 3: If the calculator has a cube function, press it to calculate 517³.

Step 4: If there is no cube function on the calculator, simply multiply 517 three times manually.

Step 5: The calculator will display 137,078,213.

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 can be expressed as the cube of an integer. For example, 8 is a perfect cube because it is 2³.
  
   
• Volume of a Cube: The amount of space contained within a cube, calculated as the side length cubed (side³).