Cube of 130

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 multiplying a negative number by itself three times results in a negative number.

The cube of 130 can be written as \(130^3\), which is the exponential form.

Or, it can also be written in arithmetic form as \(130 \times 130 \times 130\).

To check whether a number is a cube number or not, we can use three methods: multiplication method, a factor formula (\(a^3\)), or by using a calculator. These methods help calculate the cube faster and easier without confusion while evaluating the answer.

• By Multiplication Method 
   
• Using a Formula
   
• Using a Calculator

The multiplication method in mathematics is 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. \[130^3 = 130 \times 130 \times 130\]

Step 2: You get 2,197,000 as the answer. Hence, the cube of 130 is 2,197,000.

The formula \((a + b)^3\) is a binomial formula for finding the cube of a number. The formula is expanded as \(a^3 + 3a^2b + 3ab^2 + b^3\).

Step 1: Split the number 130 into two parts. Let \(a = 100\) and \(b = 30\), so \(a + b = 130\).

Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\).

Step 3: Calculate each term: \(a^3 = 100^3\) \(3a^2b = 3 \times 100^2 \times 30\) \(3ab^2 = 3 \times 100 \times 30^2\) \(b^3 = 30^3\)

Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((100 + 30)^3 = 100^3 + 3 \times 100^2 \times 30 + 3 \times 100 \times 30^2 + 30^3\) \(130^3 = 1,000,000 + 900,000 + 270,000 + 27,000\) \(130^3 = 2,197,000\)

Step 5: Hence, the cube of 130 is 2,197,000.

To find the cube of 130 using a calculator, input the number 130 and use the cube function (if available), or multiply \(130 \times 130 \times 130\). This operation calculates the value of \(130^3\), resulting in 2,197,000. 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 3 and 0.

Step 3: If the calculator has a cube function, press it to calculate \(130^3\).

Step 4: If there is no cube function on the calculator, simply multiply 130 three times manually.

Step 5: The calculator will display 2,197,000.

• 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: 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, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. 
   
• Perfect Cube: A number that can be expressed as the cube of an integer. 
   
• Volume of a Cube: The amount of space inside a cube, calculated as the side length cubed (\(\text{Side}^3\)).