Cube of 77

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 77 can be written as (77³), which is the exponential form.

Or it can also be written in arithmetic form as, 77 × 77 × 77.

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. 77³ = 77 × 77 × 77

Step 2: You get 456,533 as the answer. Hence, the cube of 77 is 456,533.

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 77 into two parts. Let (a = 70) and (b = 7), so (a + b = 77).

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

Step 3: Calculate each term a³ = 70³ 3a²b = 3 × 70²× 7, 3ab² = 3× 70× 7² b³ = 7³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ 

(70 + 7)³ = 70³ + 3 × 70² × 7 + 3 × 70 × 7² + 7³ (77³ = 343000 + 102900 + 10290 + 343) (77³ = 456,533)

Step 5: Hence, the cube of 77 is 456,533.

To find the cube of 77 using a calculator, input the number 77 and use the cube function (if available) or multiply 77 × 77 × 77. This operation calculates the value of 77³, resulting in 456,533. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 7 followed by 7

Step 3: If the calculator has a cube function, press it to calculate 77³.

Step 4: If there is no cube function on the calculator, simply multiply 77 three times manually.

Step 5: The calculator will display 456,533.

• 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

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

• Volume of a Cube: It refers to the amount of space occupied by a cube and is calculated by raising the side length to the power of three V = Side³.