Cube of -125

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 -125 can be written as (-125)^3, which is the exponential form. Or it can also be written in arithmetic form as, (-125) × (-125) × (-125).

To check whether a number is a cube number or not, we can use the following three methods: multiplication method, factor formula (a^3), or by using a calculator. These three methods will help you cube 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 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. (-125)^3 = (-125) × (-125) × (-125) Step 2: You get -1,953,125 as the answer. Hence, the cube of -125 is -1,953,125.

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 -125 into two parts, such as -100 and -25. Let a = -100 and b = -25, so a + b = -125 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-100)^3 3a^2b = 3 × (-100)^2 × (-25) 3ab^2 = 3 × (-100) × (-25)^2 b^3 = (-25)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-100 + -25)^3 = (-100)^3 + 3 × (-100)^2 × (-25) + 3 × (-100) × (-25)^2 + (-25)^3 (-125)^3 = -1,000,000 + 750,000 + 187,500 - 15,625 (-125)^3 = -1,953,125 Step 5: Hence, the cube of -125 is -1,953,125.

To find the cube of -125 using a calculator, input the number -125 and use the cube function (if available) or multiply (-125) × (-125) × (-125). This operation calculates the value of (-125)^3, resulting in -1,953,125. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -125 Step 3: If the calculator has a cube function, press it to calculate (-125)^3. Step 4: If there is no cube function on the calculator, simply multiply -125 three times manually. Step 5: The calculator will display -1,953,125.

- The cube of any negative number is always negative, while the cube of any positive number is always positive. - 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. For example, 2^3 represents 2 × 2 × 2 equals 8. - Perfect Cube: A number that is the result of an integer multiplied by itself twice more. - Cube Root: A number that when multiplied by itself three times gives the original number. For example, the cube root of -125 is -5.