Cube of 490

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 490 can be written as 490³, which is the exponential form. Or it can also be written in arithmetic form as, 490 × 490 × 490.

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 by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number. 490³ = 490 × 490 × 490

Step 2: You get 117,649,000 as the answer. Hence, the cube of 490 is 117,649,000.

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 490 into two parts. Let a = 400 and b = 90, so a + b = 490

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

Step 3: Calculate each term a³ = 400³

3a²b = 3 × 400² × 90

3ab² = 3 × 400 × 90²

b³ = 90³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(400 + 90)³ = 400³ + 3 × 400² × 90 + 3 × 400 × 90² + 90³

490³ = 64,000,000 + 43,200,000 + 9,720,000 + 729,000

490³ = 117,649,000

Step 5: Hence, the cube of 490 is 117,649,000.

To find the cube of 490 using a calculator, input the number 490 and use the cube function (if available) or multiply 490 × 490 × 490. This operation calculates the value of 490³, resulting in 117,649,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 4 followed by 9 and 0

Step 3: If the calculator has a cube function, press it to calculate 490³.

Step 4: If there is no cube function on the calculator, simply multiply 490 three times manually.

Step 5: The calculator will display 117,649,000.

• 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.

• Volume: The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great. In the context of a cube, it is calculated as side³.