Cube of 987

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 because a negative number multiplied by itself three times results in a negative number.

The cube of 987 can be expressed as 987³, which is the exponential form. Or it can also be written in arithmetic form as 987 × 987 × 987.

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, factor formula (a³), or by using a calculator. These three methods help in cubing numbers faster and easier without confusion 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 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. 987³ = 987 × 987 × 987.

Step 2: You get 961,504,803 as the answer.

Hence, the cube of 987 is 961,504,803.

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 987 into two parts.

Let a = 900 and b = 87, so a + b = 987

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

Step 3: Calculate each term

a³ = 900³

3a²b = 3 × 900² × 87

3ab² = 3 × 900 × 87²

b³ = 87³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(900 + 87)³ = 900³ + 3 × 900² × 87 + 3 × 900 × 87² + 87³

987³ = 729,000,000 + 210,690,000 + 20,439,900 + 658,503

987³ = 961,504,803.

Step 5: Hence, the cube of 987 is 961,504,803.

To find the cube of 987 using a calculator, input the number 987 and use the cube function (if available) or multiply 987 × 987 × 987. This operation calculates the value of 987³, resulting in 961,504,803. 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 8 and then 7

Step 3: If the calculator has a cube function, press it to calculate 987³.

Step 4: If there is no cube function on the calculator, simply multiply 987 three times manually.

Step 5: The calculator will display 961,504,803.

• 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.

• Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

• Perfect Cube: A number that is the cube of an integer. For example, 27 is a perfect cube because it is 3³.