Cube of 68

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 68 can be written as 68³, which is the exponential form.

Or it can also be written in arithmetic form as, (68 × 68 × 68).

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 a³, 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 (a³) 
   
• 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. 68³ = 68 × 68 × 68

Step 2: You get 314,432 as the answer.

Hence, the cube of 68 is 314,432.

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 68 into two parts, as and . Let (a = 60) and (b = 8), so (a + b = 68)

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

Step 3: Calculate each term (a³ = 60³) (3a²b = 3 × 60² × 8 (3ab² = 3 × 60 × 8²) (b³ = 8³)

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (60 + 8)³ = 60³ + 3 × 60² × 8 + 3 × 60 × 8² + 8³) (68³ = 216,000 + 86,400 + 23,040 + 512) (68³ = 314,432)

Step 5: Hence, the cube of 68 is 314,432.

To find the cube of 68 using a calculator, input the number 68 and use the cube function (if available) or multiply \(68 \times 68 \times 68\). This operation calculates the value of \(68³\), resulting in 314,432. 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

Step 3: If the calculator has a cube function, press it to calculate (68³).

Step 4: If there is no cube function on the calculator, simply multiply 68 three times manually.

Step 5: The calculator will display 314,432.

• 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 to 8.

• Cube Function: A calculator feature that allows direct calculation of a number raised to the third power.

• Perfect Cube: A number that can be expressed as the cube of an integer, such as 1, 8, 27, etc.