Cube of 686

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 686 can be written as 686³, which is the exponential form. Or it can also be written in arithmetic form as, 686 × 686 × 686.

In order 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 will help students to cube the 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. 686³ = 686 × 686 × 686

Step 2: You get 322,486,432 as the answer. Hence, the cube of 686 is 322,486,432.

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 686 into two parts. Let a = 680 and b = 6, so a + b = 686

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

Step 3: Calculate each term a³= 680³ 3a²b = 3 × 680² × 6 3ab² = 3 × 680 × 6² b³ = 6³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(680 + 6)³= 680³ + 3 × 680² × 6 + 3 × 680 × 6² + 6³

686³ = 314,432,000 + 82,080 + 7,344 + 216

686³ = 322,486,432

Step 5: Hence, the cube of 686 is 322,486,432.

To find the cube of 686 using a calculator, input the number 686 and use the cube function (if available) or multiply 686 × 686 × 686. This operation calculates the value of 686³, resulting in 322,486,432. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 6 followed by 8 and 6

Step 3: If the calculator has a cube function, press it to calculate 686³.

Step 4: If there is no cube function on the calculator, simply multiply 686 three times manually.

Step 5: The calculator will display 322,486,432.

• 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 of a Cube: The amount of space occupied by a cube, calculated as the cube of the side length, or side³.

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