Cube of 821

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 821 can be written as 821³, which is the exponential form. Or it can also be written in arithmetic form as, 821 × 821 × 821.

In order to check whether a number is a cube number or not, we can use the following three methods: 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. By Multiplication Method Using a Formula 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. 821³ = 821 × 821 × 821 Step 2: You get 553,033,061 as the answer. Hence, the cube of 821 is 553,033,061.

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 821 into two parts, as 800 and 21. Let a = 800 and b = 21, so a + b = 821 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = 800³ 3a²b = 3 × 800² × 21 3ab² = 3 × 800 × 21² b³ = 21³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (800 + 21)³ = 800³ + 3 × 800² × 21 + 3 × 800 × 21² + 21³ 821³ = 512,000,000 + 403,200 + 352,800 + 9,261 821³ = 553,033,061 Step 5: Hence, the cube of 821 is 553,033,061.

To find the cube of 821 using a calculator, input the number 821 and use the cube function (if available) or multiply 821 × 821 × 821. This operation calculates the value of 821³, resulting in 553,033,061. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 8 followed by 2 and 1 Step 3: If the calculator has a cube function, press it to calculate 821³. Step 4: If there is no cube function on the calculator, simply multiply 821 three times manually. Step 5: The calculator will display 553,033,061.

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. Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because it is 3³. Cube Root: The number that, when multiplied by itself twice, gives the original number. For example, the cube root of 8 is 2, because 2 × 2 × 2 = 8.