Cube of 767

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, as a negative number multiplied by itself three times results in a negative number.

The cube of 767 can be written as 767³, which is the exponential form. Or it can also be written in arithmetic form as 767 × 767 × 767.

To determine whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help students cube numbers faster and more easily 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. 767³ = 767 × 767 × 767

Step 2: You get 451,574,383 as the answer. Hence, the cube of 767 is 451,574,383.

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 767 into two parts. Let a = 700 and b = 67, so a + b = 767

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

Step 3: Calculate each term

a³ = 700³

3a²b = 3 × 700² × 67

3ab² = 3 × 700 × 67²

b³ = 67³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(700 + 67)³ = 700³ + 3 × 700² × 67 + 3 × 700 × 67² + 67³

767³ = 343000000 + 98742000 + 9945300 + 300763

767³ = 451,574,383

Step 5: Hence, the cube of 767 is 451,574,383.

To find the cube of 767 using a calculator, input the number 767 and use the cube function (if available) or multiply 767 × 767 × 767. This operation calculates the value of 767³, resulting in 451,574,383. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 7, 6, and 7

Step 3: If the calculator has a cube function, press it to calculate 767³.

Step 4: If there is no cube function on the calculator, simply multiply 767 three times manually.

Step 5: The calculator will display 451,574,383.

• 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, which equals 8. 

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

• Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.