Cube of 367

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 multiplied by itself three times results in a negative number.

The cube of 367 can be written as 367³, which is the exponential form.

Or it can also be written in arithmetic form as, 367 × 367 × 367.

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 more easily without feeling confused or stuck while evaluating the answers.

• By Multiplication Method
   
• Using a Formula
   
• 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. 367³ = 367 × 367 × 367

Step 2: You get 49,319,263 as the answer. Hence, the cube of 367 is 49,319,263.

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 367 into two parts, as 360 and 7. Let a = 360 and b = 7, so a + b = 367

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

Step 3: Calculate each term a³ = 360³ 3a²b = 3 × 360² × 7 3ab² = 3 × 360 × 7² b³ = 7³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (360 + 7)³ = 360³ + 3 × 360² × 7 + 3 × 360 × 7² + 7³ 367³ = 46,656,000 + 27,216 + 52,920 + 343 367³ = 49,319,263

Step 5: Hence, the cube of 367 is 49,319,263.

To find the cube of 367 using a calculator, input the number 367 and use the cube function (if available) or multiply 367 × 367 × 367. This operation calculates the value of 367³, resulting in 49,319,263. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 3, 6, followed by 7.

Step 3: If the calculator has a cube function, press it to calculate 367³.

Step 4: If there is no cube function on the calculator, simply multiply 367 three times manually.

Step 5: The calculator will display 49,319,263.

• 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.

• 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, \( 2^3 \) represents \( 2 \times 2 \times 2 \), which equals 8. 
   
• 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 Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. 
   
• Volume of a Cube: The volume of a cube is determined by cubing the length of one of its sides, using the formula \( V = \text{Side}^3 \).