Cube of 513

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 513 can be written as 513³, which is the exponential form. Or it can also be written in arithmetic form as, 513 × 513 × 513.

To check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help students cube numbers faster and more easily 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 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.

513³ = 513 × 513 × 513

Step 2: You get 135,796,257 as the answer.

Hence, the cube of 513 is 135,796,257.

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 513 into two parts.

Let a = 500 and b = 13, so a + b = 513

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

Step 3: Calculate each term a³ = 500³ , 3a²b = 3 × 500² × 13 , 3ab² = 3 × 500 × 13² , b³ = 13³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(500 + 13)³ = 500³ + 3 × 500² × 13 + 3 × 500 × 13² + 13³

513³ = 125,000,000 + 97,500 + 101,400 + 2,197

513³ = 135,796,097

Step 5: Hence, the cube of 513 is 135,796,257.

To find the cube of 513 using a calculator, input the number 513 and use the cube function (if available) or multiply 513 × 513 × 513. This operation calculates the value of 513³, resulting in 135,796,257. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 5, followed by 1 and 3.

Step 3: If the calculator has a cube function, press it to calculate 513³.

Step 4: If there is no cube function on the calculator, simply multiply 513 three times manually.

Step 5: The calculator will display 135,796,257.

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.
  
   
• Cube Root: The cube root of a number is a special value that, when multiplied by itself twice, gives the original number.
  
   
• Perfect Cube: A number that is the cube of an integer. For example, 27 is a perfect cube because it is 3³.