Cube of 425

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 425 can be written as 425³, which is the exponential form.

Or it can also be written in arithmetic form as 425 × 425 × 425.

In order to check whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help you cube numbers faster and easier without getting 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 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. 425³ = 425 × 425 × 425

Step 2: You get 76,765,625 as the answer. Hence, the cube of 425 is 76,765,625.

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 425 into two parts, as 400 and 25. Let a = 400 and b = 25, so a + b = 425

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

Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 25 3ab² = 3 × 400 × 25² b³ = 25³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 25)³ = 400³ + 3 × 400² × 25 + 3 × 400 × 25² + 25³ 425³ = 64,000,000 + 12,000,000 + 750,000 + 15,625 425³ = 76,765,625

Step 5: Hence, the cube of 425 is 76,765,625.

To find the cube of 425 using a calculator, input the number 425 and use the cube function (if available) or multiply 425 × 425 × 425. This operation calculates the value of 425³, resulting in 76,765,625. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input 425

Step 3: If the calculator has a cube function, press it to calculate 425³.

Step 4: If there is no cube function on the calculator, simply multiply 425 three times manually.

Step 5: The calculator will display 76,765,625.

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 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, 2³ represents 2 × 2 × 2, which equals 8.

• Cube Root: The number that produces a specified quantity when multiplied by itself three times.

• Perfect Cube: A number that is the cube of an integer. For example, 8 is a perfect cube because it is 2³.