Cube of 310

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 310 can be written as 310³, which is the exponential form. Or it can also be written in arithmetic form as 310 × 310 × 310.

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These methods 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 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. 310³ = 310 × 310 × 310

Step 2: Calculate the product to get 29,791,000 as the answer.

Hence, the cube of 310 is 29,791,000.

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 310 into two parts. Let a = 300 and b = 10, so a + b = 310

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

Step 3: Calculate each term a³ = 300³ 3a²b = 3 × 300² × 10 3ab² = 3 × 300 × 10² b³ = 10³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(300 + 10)³ = 300³ + 3 × 300² × 10 + 3 × 300 × 10² + 10³

310³ = 27,000,000 + 2,700,000 + 90,000 + 1,000

310³ = 29,791,000

Step 5: Hence, the cube of 310 is 29,791,000.

To find the cube of 310 using a calculator, input the number 310 and use the cube function (if available) or multiply 310 × 310 × 310. This operation calculates the value of 310³, resulting in 29,791,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input 310.

Step 3: If the calculator has a cube function, press it to calculate 310³.

Step 4: If there is no cube function on the calculator, simply multiply 310 three times manually.

Step 5: The calculator will display 29,791,000.

• 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, 2³ represents 2 × 2 × 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.