Cube of 175

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 because a negative number multiplied by itself three times results in a negative number.

The cube of 175 can be written as 175³, which is the exponential form, or it can also be written in arithmetic form as 175 × 175 × 175.

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 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. 175³ = 175 × 175 × 175

Step 2: You get 5,359,375 as the answer. Hence, the cube of 175 is 5,359,375.

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 175 into two parts, as 150 and 25. Let a = 150 and b = 25, so a + b = 175

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

Step 3: Calculate each term a³ = 150³ 3a²b = 3 × 150² × 25 3ab² = 3 × 150 × 25² b³ = 25³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(150 + 25)³ = 150³ + 3 × 150² × 25 + 3 × 150 × 25² + 25³

175³ = 3,375,000 + 1,687,500 + 281,250 + 15,625

175³ = 5,359,375

Step 5: Hence, the cube of 175 is 5,359,375.

To find the cube of 175 using a calculator, input the number 175 and use the cube function (if available) or multiply 175 × 175 × 175. This operation calculates the value of 175³, resulting in 5,359,375. 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 7 and 5

Step 3: If the calculator has a cube function, press it to calculate 175³.

Step 4: If there is no cube function on the calculator, simply multiply 175 three times manually.

Step 5: The calculator will display 5,359,375.

• 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: 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, which equals 8.

• Volume of a Cube: The amount of space inside a cube, calculated as Side³, where the side is the length of one edge of the cube.

• Perfect Cube: A number that is the cube of an integer. For example, 8 is a perfect cube because it equals 2 × 2 × 2.