Cube of 413

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 413 can be written as 413³, which is the exponential form.

Or it can also be written in arithmetic form as, 413 × 413 × 413.

In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

• By Multiplication Method
   
• Using a Formula (a³)
   
• 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. 413³ = 413 × 413 × 413

Step 2: You get 70,381,997 as the answer. Hence, the cube of 413 is 70,381,997.

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 413 into two parts, as 400 and 13. Let a = 400 and b = 13, so a + b = 413

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

Step 3: Calculate each term a^3 = 400^3 3a^2b = 3 × 400^2 × 13 3ab^2 = 3 × 400 × 13^2 b^3 = 13^3

Step 4: Add all the terms together: (a + b)^3 = a³ + 3a²b + 3ab² + b³ (400 + 13)³ = 400³ + 3 × 400² × 13 + 3 × 400 × 13² + 13³ 413³ = 64,000,000 + 6,240,000 + 202,800 + 2,197 413³ = 70,381,997

Step 5: Hence, the cube of 413 is 70,381,997.

To find the cube of 413 using a calculator, input the number 413 and use the cube function (if available) or multiply 413 × 413 × 413. This operation calculates the value of 413^3, resulting in 70,381,997. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input 413

Step 3: If the calculator has a cube function, press it to calculate 413^3.

Step 4: If there is no cube function on the calculator, simply multiply 413 three times manually.

Step 5: The calculator will display 70,381,997.

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, 3³ represents 3 × 3 × 3 equals 27.

• Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted as ∛x.

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