Cube of 478

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 478 can be written as 478³, which is the exponential form. Or it can also be written in arithmetic form as, 478 × 478 × 478.

To check whether a number is a cube number or not, we can use the following methods: multiplication method, a factor formula (a³), or by using a calculator. These methods will help compute the cube of numbers faster and easier without confusion.

1. By Multiplication Method
2. Using a Formula
3. Using a Calculator

The multiplication method is a mathematical process used to find the product of numbers by repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number. 478³ = 478 × 478 × 478

Step 2: You get 109,938,952 as the answer. Hence, the cube of 478 is 109,938,952.

The formula (a + b)³ is a binomial formula used to find the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.

Step 1: Split the number 478 into two parts, such as a and b. Let a = 400 and b = 78, so a + b = 478

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

Step 3: Calculate each term

a³ = 400³

3a²b = 3 × 400² × 78

3ab² = 3 × 400 × 78²

b³ = 78³

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

(400 + 78)³ = 400³ + 3 × 400² × 78 + 3 × 400 × 78² + 78³

478³ = 64,000,000 + 37,440,000 + 7,286,400 + 474,552

478³ = 109,938,952

Step 5: Hence, the cube of 478 is 109,938,952.

To find the cube of 478 using a calculator, input the number 478 and use the cube function (if available) or multiply 478 × 478 × 478. This operation calculates the value of 478³, resulting in 109,938,952. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 478

Step 3: If the calculator has a cube function, press it to calculate 478³.

Step 4: If there is no cube function, simply multiply 478 three times manually.

Step 5: The calculator will display 109,938,952.

• 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: 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: 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 third power (side³).

• Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2, because 2 × 2 × 2 = 8.