Cube of 1314

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 1314 can be written as 1314³, which is the exponential form. Or it can also be written in arithmetic form as 1314 x 1314 x 1314).

In order to check whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator.

These three methods will help students cube the numbers 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. 1314³ = 1314 x 1314 x 1314

Step 2: You get 2,269,239,144 as the answer. Hence, the cube of 1314 is 2,269,239,144.

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 1314 into two parts. Let a = 1300 and b = 14, so a + b = 1314.

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3a^b2 + b³.

Step 3: Calculate each term: a³ = 1300³

3a²b = 3 x 1300² x 14

3ab² = 3 x 1300 x 14²

b³ = 14³

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

(1300 + 14)³ = 1300³ + 3 x 1300² x 14 + 3 x 1300 x 14² + 14³

1314³ = 2,197,000,000 + 70,980,000 + 3,412,800 + 2,744

1314³ = 2,269,239,144

Step 5: Hence, the cube of 1314 is 2,269,239,144.

To find the cube of 1314 using a calculator, input the number 1314 and use the cube function (if available) or multiply 1314 x 1314 x 1314. This operation calculates the value of 1314³, resulting in 2,269,239,144. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 1314.

Step 3: If the calculator has a cube function, press it to calculate 1314³.

Step 4: If there is no cube function on the calculator, simply multiply 1314 three times manually.

Step 5: The calculator will display 2,269,239,144.

• 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 x 2 x 2 equals 8. 

• Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because 3³ = 27. 

• Volume of a Cube: The amount of space enclosed within a cube, calculated as the side length raised to the power of three.