Cube of 851

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 851 can be written as 851³, which is the exponential form. Or it can also be written in arithmetic form as 851 × 851 × 851.

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.

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. 851³ = 851 × 851 × 851

Step 2: Calculate the product to get 616,298,301 as the answer. Hence, the cube of 851 is 616,298,301.

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 851 into two parts. Let a = 850 and b = 1, so a + b = 851.

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

Step 3: Calculate each term:

a³ = 850³

3a²b = 3 × 850² × 1

3ab² = 3 × 850 × 1²

b³ = 1³

Step 4: Add all the terms together:

(850 + 1)³ = 850³ + 3 × 850² × 1 + 3 × 850 × 1² + 1³

851³ = 614,125,000 + 2,167,500 + 2,550 + 1

851³ = 616,298,301

Step 5: Hence, the cube of 851 is 616,298,301.

To find the cube of 851 using a calculator, input the number 851 and use the cube function (if available) or multiply 851 × 851 × 851. This operation calculates the value of 851³, resulting in 616,298,301. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 851.

Step 3: If the calculator has a cube function, press it to calculate 851³.

Step 4: If there is no cube function on the calculator, simply multiply 851 three times manually.

Step 5: The calculator will display 616,298,301.

• 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: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer. 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: 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.

• Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted as ∛x.

• Volume of a Cube: The amount of space inside a cube, calculated as the cube of its side length, V = Side³.