Cube of -125
2026-02-28 10:32 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-minus-125

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Last updated on August 5, 2025

When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of -125.

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).

How to Calculate the Value of the Cube of -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

By Multiplication Method

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.

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Using a Formula (a^3)

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.

Using a Calculator

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.

Tips and Tricks for the Cube of -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.

Common Mistakes to Avoid When Calculating the Cube of -125

There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:

Problem 1

What is the cube and cube root of -125?

Okay, lets begin

The cube of -125 is -1,953,125 and the cube root of -125 is -5.

Explanation

First, let’s find the cube of -125. We know that the cube of a number, such that x^3 = y Where x is the given number, and y is the cubed value of that number. So, we get (-125)^3 = -1,953,125 Next, we must find the cube root of -125 We know that the cube root of a number ‘x’, such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number. So, we get ∛(-125) = -5 Hence, the cube of -125 is -1,953,125 and the cube root of -125 is -5.

Well explained 👍

Problem 2

If the side length of a cube is -125 cm, what is the volume?

Okay, lets begin

The volume is -1,953,125 cm³.

Explanation

Use the volume formula for a cube V = Side^3. Substitute -125 for the side length: V = (-125)^3 = -1,953,125 cm³.

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Problem 3

How much larger is (-125)^3 than (-100)^3?

Okay, lets begin

(-125)^3 - (-100)^3 = -953,125.

Explanation

First, find the cube of (-125), that is -1,953,125 Next, find the cube of (-100), which is -1,000,000 Now, find the difference between them using the subtraction method. -1,953,125 - (-1,000,000) = -953,125 Therefore, (-125)^3 is -953,125 larger than (-100)^3.

Well explained 👍

Problem 4

If a cube with a side length of -125 cm is compared to a cube with a side length of -25 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of -125 cm is -1,953,125 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -125 means multiplying -125 by itself three times: -125 × -125 = 15,625, and then 15,625 × -125 = -1,953,125. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is -1,953,125 cm³.

Well explained 👍

Problem 5

Estimate the cube of -124.9 using the cube of -125.

Okay, lets begin

The cube of -124.9 is approximately -1,953,125.

Explanation

First, identify the cube of -125, The cube of -125 is (-125)^3 = -1,953,125. Since -124.9 is very close to -125, the cube of -124.9 will be almost the same as the cube of -125. The cube of -124.9 is approximately -1,953,125 because the difference between -124.9 and -125 is very small. So, we can approximate the value as -1,953,125.

Well explained 👍

FAQs on Cube of -125

1.What are the perfect cubes up to -125?

The perfect cubes up to -125 are -1, -8, and -27.

2.How do you calculate (-125)^3?

To calculate (-125)^3, use the multiplication method, (-125) × (-125) × (-125), which equals -1,953,125.

3.What is the meaning of (-125)^3?

(-125)^3 means -125 multiplied by itself three times, or (-125) × (-125) × (-125).

4.What is the cube root of -125?

5.Is -125 a perfect cube?

Yes, -125 is a perfect cube because the integer -5 multiplied by itself three times equals -125.

Important Glossaries for Cube of -125

- 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.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.