Cube of 475

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 475 can be written as 475³, which is the exponential form. Or it can also be written in arithmetic form as 475 × 475 × 475.

To determine 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 to cube 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 mathematical process 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. 475³ = 475 × 475 × 475

Step 2: You get 107,171,875 as the answer. Hence, the cube of 475 is 107,171,875.

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 475 into two parts, such as a and b. Let a = 470 and b = 5, so a + b = 475

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

Step 3: Calculate each term a³ = 470³ 3a²b = 3 × 470² × 5 3ab² = 3 × 470 × 5² b³ = 5³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(470 + 5)³ = 470³ + 3 × 470² × 5 + 3 × 470 × 5² + 5³

475³ = 103823000 + 3315000 + 35250 + 125

475³ = 107171875

Step 5: Hence, the cube of 475 is 107,171,875.

To find the cube of 475 using a calculator, input the number 475 and use the cube function (if available) or multiply 475 × 475 × 475. This operation calculates the value of 475³, resulting in 107,171,875. 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 7 and 5.

Step 3: If the calculator has a cube function, press it to calculate 475³.

Step 4: If there is no cube function on the calculator, simply multiply 475 three times manually.

Step 5: The calculator will display 107,171,875.

• 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 Formula: The formula used to determine the space inside a 3D object, calculated as side³ for cubes.

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