Cube of 462

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 462 can be written as 462³, which is the exponential form. Or it can also be written in arithmetic form as, 462 × 462 × 462.

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 the 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.

462³ = 462 × 462 × 462

Step 2: You get 98,304,328 as the answer.

Hence, the cube of 462 is 98,304,328.

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 462 into two parts.

Let a = 460 and b = 2, so a + b = 462

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

Step 3: Calculate each term

a³ = 460³

3a²b = 3 × 460² × 2

3ab² = 3 × 460 × 2²

b³ = 2³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(460 + 2)³ = 460³ + 3 × 460² × 2 + 3 × 460 × 2² + 2³

462³ = 97,336,000 + 1,267,200 + 5,520 + 8

462³ = 98,608,728

Step 5: Hence, the cube of 462 is 98,608,728.

To find the cube of 462 using a calculator, input the number 462 and use the cube function (if available) or multiply 462 × 462 × 462. This operation calculates the value of 462³, resulting in 98,608,728. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 4, 6, 2

Step 3: If the calculator has a cube function, press it to calculate 462³.

Step 4: If there is no cube function on the calculator, simply multiply 462 three times manually.

Step 5: The calculator will display 98,608,728.

• 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.

• Volume of a Cube: The amount of space occupied by a cube, calculated as the side length raised to the power of 3.

• Cube Root: The number which produces a given number when cubed. For example, the cube root of 8 is 2 since 2³ = 8.