Cube of 126

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 126 can be written as 126³, which is the exponential form.

Or it can also be written in arithmetic form as, 126 × 126 × 126.

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 
   
• 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. \(126³ = 126 × 126 × 126\)

Step 2: You get 2,000,376 as the answer. Hence, the cube of 126 is 2,000,376.

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 126 into two parts. Let a = 120 and b = 6, so a + b = 126

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

Step 3: Calculate each term \(a³= 120³\) \(3a²b = 3 × 120² × 6\) \(3ab² = 3 × 120 × 6²\) \(b³ = 6³\)

Step 4: Add all the terms together: \((a + b)³ = a³ + 3a²b + 3ab² + b³\) \((120 + 6)³= 120³ + 3 × 120² × 6 + 3 × 120 × 6² + 6³\) \(126³ = 1,728,000 + 259,200 + 25,920 + 216\) \(126³ = 2,000,376\)

Step 5: Hence, the cube of 126 is 2,000,376.

To find the cube of 126 using a calculator, input the number 126 and use the cube function (if available) or multiply 126 × 126 × 126. This operation calculates the value of 126³, resulting in 2,000,376. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1 followed by 2 then 6

Step 3: If the calculator has a cube function, press it to calculate 126³.

Step 4: If there is no cube function on the calculator, simply multiply 126 three times manually.

Step 5: The calculator will display 2,000,376.

• 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 helps 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.
   
• Multiplication Method: A process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition.
   
• Perfect Cube: A number that can be expressed as the cube of an integer.