Cube of -2744

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 -2744 can be written as \((-2744)^3\), which is the exponential form.

Or it can also be written in arithmetic form as, \(-2744 \times -2744 \times -2744\).

To verify whether a number is a cube number, we can use the following three methods: the multiplication method, a factor formula (\(a^3\)), or by using a calculator. These methods will help compute the cube of numbers faster and easier without confusion or errors during evaluation.

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

The multiplication method is a process in mathematics used to find the product of numbers 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. \((-2744)^3 = -2744 \times -2744 \times -2744\)

Step 2: The answer is -20,582,542,016. Hence, the cube of -2744 is -20,582,542,016.

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 -2744 into two parts, as \(a\) and \(b\). Let \(a = -2700\) and \(b = -44\), so \(a + b = -2744\)

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

Step 3: Calculate each term \(a^3 = (-2700)^3\) \(3a^2b = 3 \times (-2700)^2 \times (-44)\) \(3ab^2 = 3 \times (-2700) \times (-44)^2\) \(b^3 = (-44)^3\)

Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((-2700 + -44)^3 = (-2700)^3 + 3 \times (-2700)^2 \times (-44) + 3 \times (-2700) \times (-44)^2 + (-44)^3\) \((-2744)^3 = -19,683,000,000 + 10,594,560,000 + 15,830,400 + -85,184\) \((-2744)^3 = -20,582,542,016\)

Step 5: Hence, the cube of -2744 is -20,582,542,016.

To find the cube of -2744 using a calculator, input the number -2744 and use the cube function (if available) or multiply \(-2744 \times -2744 \times -2744\). This operation calculates the value of \((-2744)^3\), resulting in -20,582,542,016. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input -2744.

Step 3: If the calculator has a cube function, press it to calculate \((-2744)^3\).

Step 4: If there is no cube function on the calculator, simply multiply -2744 three times manually.

Step 5: The calculator will display -20,582,542,016.

• 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.

• 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, \(2^3\) represents \(2 \times 2 \times 2\) equals to 8.
   
• 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.
   
• Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because it can be expressed as \(3^3\).
   
• Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.