Cube of 150

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

The cube of 150 can be written as 150³, which is the exponential form. Or it can also be written in arithmetic form as, 150 × 150 × 150.

In order to check whether a number is a cube number or not, we can use the following three methods, such as 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 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. 150³ = 150 × 150 × 150

Step 2: You get 3,375,000 as the answer. Hence, the cube of 150 is 3,375,000.

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 150 into two parts, as a and b. Let a = 100 and b = 50, so a + b = 150

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

  Calculate each term a³ = 100³ 3a²b = 3 × 100² × 50 3ab² = 3 × 100 × 50² b³ = 50³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(100 + 50)³ = 100³ + 3 × 100² × 50 + 3 × 100 × 50² + 50³

150³ = 1,000,000 + 1,500,000 + 750,000 + 125,000

150³ = 3,375,000

Step 5: Hence, the cube of 150 is 3,375,000.

To find the cube of 150 using a calculator, input the number 150 and use the cube function (if available) or multiply 150 × 150 × 150. This operation calculates the value of 150³, resulting in 3,375,000. 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 5 and 0

Step 3: If the calculator has a cube function, press it to calculate 150³.

Step 4: If there is no cube function on the calculator, simply multiply 150 three times manually.

Step 5: The calculator will display 3,375,000.

• 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: 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.

• Perfect Cube: A number that can be expressed as the cube of an integer. For instance, 27 is a perfect cube because it equals 3 × 3 × 3.

• Cube Root: The cube root of a number is a value that, when cubed, gives the original number. It is denoted as ∛x, where x is the original number.