Cube of 421

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 421 can be written as 421³, which is the exponential form.

Or it can also be written in arithmetic form as 421 × 421 × 421.

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 kids to cube numbers faster and easier 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 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. 421³ = 421 × 421 × 421

Step 2: You get 74,792,761 as the answer. Hence, the cube of 421 is 74,792,761.

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 421 into two parts. Let a = 420 and b = 1, so a + b = 421

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

Step 3: Calculate each term: a³ = 420³ 3a²b = 3 × 420² × 1 3ab² = 3 × 420 × 1² b³ = 1³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (420 + 1)³ = 420³ + 3 × 420² × 1 + 3 × 420 × 1² + 1³ 421³ = 74,088,000 + 529,200 + 1,260 + 1 421³ = 74,792,761

Step 5: Hence, the cube of 421 is 74,792,761.

To find the cube of 421 using a calculator, input the number 421 and use the cube function (if available) or multiply 421 × 421 × 421. This operation calculates the value of 421³, resulting in 74,792,761. 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 2, then 1.

Step 3: If the calculator has a cube function, press it to calculate 421³.

Step 4: If there is no cube function on the calculator, simply multiply 421 three times manually.

Step 5: The calculator will display 74,792,761.

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, which equals 8.

• Volume of a Cube: The amount of space enclosed within a cube, calculated as Side³.

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