Cube of 682

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 682 can be written as 682³, which is the exponential form. Or it can also be written in arithmetic form as 682 × 682 × 682.

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 three methods will help calculate cube numbers faster and easier without confusion.

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 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. 682³ = 682 × 682 × 682

Step 2: Calculate the answer. After multiplication, you get 317,652,368 as the answer.

Hence, the cube of 682 is 317,652,368.

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 682 into two parts, such as 680 and 2. Let a = 680 and b = 2, so a + b = 682

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

Step 3: Calculate each term

a³ = 680³

3a²b = 3 × 680² × 2

3ab² = 3 × 680 × 2²

b³ = 2³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(680 + 2)³ = 680³ + 3 × 680² × 2 + 3 × 680 × 2² + 2³

682³ = 314,432,000 + 2,774,400 + 8,160 + 8

682³ = 317,652,368

Step 5: Hence, the cube of 682 is 317,652,368.

To find the cube of 682 using a calculator, input the number 682 and use the cube function (if available) or multiply 682 × 682 × 682. This operation calculates the value of 682³, resulting in 317,652,368. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 682

Step 3: If the calculator has a cube function, press it to calculate 682³.

Step 4: If there is no cube function on the calculator, simply multiply 682 three times manually.

Step 5: The calculator will display 317,652,368.

• 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.

• Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice.

• Volume of a Cube: The amount of space inside a cube, calculated as the side length raised to the third power.