Cube of 900

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 900 can be written as 900³, which is the exponential form. Or it can also be written in arithmetic form as, 900 × 900 × 900.

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 (\(a^3\)), 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.

900³ = 900 × 900 × 900

Step 2: Calculate the result to get 729,000,000 as the answer.

Hence, the cube of 900 is 729,000,000.

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 900 into two parts, as 800 and 100.

Let a = 800 and b = 100, so a + b = 900

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

Step 3: Calculate each term

a³ = 800³

3a²b = 3 × 800² × 100

3ab² = 3 × 800 × 100²

b³ = 100³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(800 + 100)³ = 800³ + 3 × 800² × 100 + 3 × 800 × 100² + 100³

900³ = 512,000,000 + 192,000,000 + 24,000,000 + 1,000,000

900³ = 729,000,000

Step 5: Hence, the cube of 900 is 729,000,000.

To find the cube of 900 using a calculator, input the number 900 and use the cube function (if available) or multiply 900 × 900 × 900. This operation calculates the value of 900³, resulting in 729,000,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 9 followed by 0 and 0.

Step 3: If the calculator has a cube function, press it to calculate 900³.

Step 4: If there is no cube function on the calculator, simply multiply 900 three times manually.

Step 5: The calculator will display 729,000,000.

• 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, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. Perfect Cube: A number that can be expressed as the cube of an integer. Volume: The amount of space that a substance or object occupies or that is enclosed within a container, especially when great. For a cube, it is calculated as side length cubed.