Cube of 735

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 735 can be written as \(735^3\), which is the exponential form. Or it can also be written in arithmetic form as, \(735 \times 735 \times 735\).

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula \((a^3)\), or by using a calculator. These three methods will help calculate the cube of 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. \[735^3 = 735 \times 735 \times 735\] Step 2: You get 397,431,375 as the answer. Hence, the cube of 735 is 397,431,375.

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 735 into two parts. Let \(a = 700\) and \(b = 35\), so \(a + b = 735\) Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) Step 3: Calculate each term \(a^3= 700^3\) \(3a^2b = 3 \times 700^2 \times 35\) \(3ab^2 = 3 \times 700 \times 35^2\) \(b^3 = 35^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((700 + 35)^3 = 700^3 + 3 \times 700^2 \times 35 + 3 \times 700 \times 35^2 + 35^3\) \(735^3 = 343,000,000 + 51,450,000 + 2,572,500 + 42,875\) \(735^3 = 397,431,375\) Step 5: Hence, the cube of 735 is 397,431,375.

To find the cube of 735 using a calculator, input the number 735 and use the cube function (if available) or multiply \(735 \times 735 \times 735\). This operation calculates the value of \(735^3\), resulting in 397,431,375. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 7, 3, and 5 Step 3: If the calculator has a cube function, press it to calculate \(735^3\). Step 4: If there is no cube function on the calculator, simply multiply 735 three times manually. Step 5: The calculator will display 397,431,375.

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 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. For example, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. Perfect Cube: A number that is the cube of an integer. For example, \(27\) is a perfect cube because \(3 \times 3 \times 3 = 27\). Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3, because \(3 \times 3 \times 3 = 27\).