Cube of 213

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 213 can be written as \(213^3\), which is the exponential form. Or it can also be written in arithmetic form as, \(213 \times 213 \times 213\).

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 (\(a^3\)), 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 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. \(213^3 = 213 \times 213 \times 213\) Step 2: You get 9,665,157 as the answer. Hence, the cube of 213 is 9,665,157.

The formula (\(a + b\))^3 is a binomial formula for finding the cube of a number. The formula is expanded as \(a^3 + 3a^2b + 3ab^2 + b^3\). Step 1: Split the number 213 into two parts, as 200 and 13. Let \(a = 200\) and \(b = 13\), so \(a + b = 213\). Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). Step 3: Calculate each term \(a^3= 200^3\) \(3a^2b = 3 \times 200^2 \times 13\) \(3ab^2 = 3 \times 200 \times 13^2\) \(b^3 = 13^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((200 + 13)^3 = 200^3 + 3 \times 200^2 \times 13 + 3 \times 200 \times 13^2 + 13^3\) \(213^3 = 8,000,000 + 1,560,000 + 101,400 + 2,197\) \(213^3 = 9,665,157\) Step 5: Hence, the cube of 213 is 9,665,157.

To find the cube of 213 using a calculator, input the number 213 and use the cube function (if available) or multiply \(213 \times 213 \times 213\). This operation calculates the value of \(213^3\), resulting in 9,665,157. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 2, followed by 1, and then 3. Step 3: If the calculator has a cube function, press it to calculate \(213^3\). Step 4: If there is no cube function on the calculator, simply multiply 213 three times manually. Step 5: The calculator will display 9,665,157.

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, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of its side length. Perfect Cube: A number that can be expressed as the cube of an integer.