Cube of 674

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 674 can be written as 674³, which is the exponential form. Or it can also be written in arithmetic form as, 674 × 674 × 674.

In order to check whether a number is a cube number or not, we can use the following three methods, such as the 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.

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. 674³ = 674 × 674 × 674

Step 2: You get 306,844,024 as the answer. Hence, the cube of 674 is 306,844,024.

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 674 into two parts. Let a = 670 and b = 4, so a + b = 674

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

Step 3: Calculate each term

a³ = 670³

3a²b = 3 × 670² × 4

3ab² = 3 × 670 × 4²

b³ = 4³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(670 + 4)³ = 670³ + 3 × 670² × 4 + 3 × 670 × 4² + 4³

674³ = 301,563,000 + 5,382,400 + 32,160 + 64

674³ = 306,844,024

Step 5: Hence, the cube of 674 is 306,844,024.

To find the cube of 674 using a calculator, input the number 674 and use the cube function (if available) or multiply 674 × 674 × 674. This operation calculates the value of 674³, resulting in 306,844,024. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input 674.

Step 3: If the calculator has a cube function, press it to calculate 674³.

Step 4: If there is no cube function on the calculator, simply multiply 674 three times manually.

Step 5: The calculator will display 306,844,024.

• 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 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.

• Volume: The amount of space occupied by a 3-dimensional object, measured in cubic units. For a cube, it is calculated as side³.

• Cube Root: The value that, when cubed, gives the original number. For example, the cube root of 27 is 3, because 3³ = 27.