Cube of 702

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 702 can be written as 702³, which is the exponential form. Or it can also be written in arithmetic form as, 702 × 702 × 702.

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. 702³ = 702 × 702 × 702

Step 2: Calculate the multiplication to get the answer. 702 × 702 = 492,804 492,804 × 702 = 345,911,208

Hence, the cube of 702 is 345,911,208.

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 702 into two parts, as a and b. Let a = 700 and b = 2, so a + b = 702

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

Step 3: Calculate each term a³ = 700³ 3a²b = 3 × 700² × 2 3ab² = 3 × 700 × 2² b³ = 2³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(700 + 2)³ = 700³ + 3 × 700² × 2 + 3 × 700 × 2² + 2³

700³ = 343,000,000 3 × 700² × 2 = 2,940,000 3 × 700 × 2² = 8,400 2³ = 8

Step 5: Add all terms:

702³ = 343,000,000 + 2,940,000 + 8,400 + 8 702³ = 345,911,208

Hence, the cube of 702 is 345,911,208.

To find the cube of 702 using a calculator, input the number 702 and use the cube function (if available) or multiply 702 × 702 × 702. This operation calculates the value of 702³, resulting in 345,911,208. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 7 followed by 0 and 2

Step 3: If the calculator has a cube function, press it to calculate 702³.

Step 4: If there is no cube function on the calculator, simply multiply 702 three times manually.

Step 5: The calculator will display 345,911,208.

• 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 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: 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.

• Cube Root: The number that produces a given number when cubed. For example, the cube root of 8 is 2, as 2³ = 8.

• Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because it can be expressed as 3³.