Cube of 178

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 178 can be written as 178³, which is the exponential form. Or it can also be written in arithmetic form as, 178 × 178 × 178.

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 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. 178³ = 178 × 178 × 178

Step 2: You get 5,648,952 as the answer. Hence, the cube of 178 is 5,648,952.

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 178 into two parts, for example, as 170 and 8.

Let a = 170 and b = 8, so a + b = 178

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

Step 3: Calculate each term a³ = 170³ 3a²b = 3 × 170² × 8 3ab² = 3 × 170 × 8² b³ = 8³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³

(170 + 8)³ = 170³ + 3 × 170² × 8 + 3 × 170 × 8² + 8³

178³ = 4,913,000 + 554,880 + 32,640 + 512

178³ = 5,648,952

Step 5: Hence, the cube of 178 is 5,648,952.

To find the cube of 178 using a calculator, input the number 178 and use the cube function (if available) or multiply 178 × 178 × 178. This operation calculates the value of 178³, resulting in 5,648,952. 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 8

Step 3: If the calculator has a cube function, press it to calculate 178³.

Step 4: If there is no cube function on the calculator, simply multiply 178 three times manually.

Step 5: The calculator will display 5,648,952.

• 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 equals 8.

• Volume: The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great. For a cube, it is calculated as the cube of its side length.

• Perfect Cube: A number that can be expressed as the cube of an integer. Examples include 1, 8, 27, 64, and 125.