Last updated on May 26th, 2025
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of -125 and explain the methods used.
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In exponential form, ∛-125 is written as (-125)^(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of -125, then y^3 can be -125. The cube root of -125 is exactly -5, because (-5) × (-5) × (-5) = -125.
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of -125. The common methods we follow to find the cube root are given below: Prime factorization method Approximation method Subtraction method Halley’s method Since -125 is a perfect cube, we can use the prime factorization method to find the cube root.
Let's find the cube root of -125 using the prime factorization method. First, find the prime factors of -125: -125 = -1 × 5 × 5 × 5 To find the cube root, group the factors in triples: ∛(-1 × 5 × 5 × 5) = -5 Therefore, the cube root of -125 is -5, since (-5) × (-5) × (-5) = -125.
Finding the perfect cube root of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Imagine you have a cube-shaped toy that has a total volume of -125 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛-125 = -5 units
To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is exactly -5 units.
A company manufactures -125 cubic meters of a material. Calculate the amount of material left after using -50 cubic meters.
The amount of material left is -75 cubic meters.
To find the remaining material, subtract the used material from the total amount: -125 - (-50) = -125 + 50 = -75 cubic meters.
A bottle holds -125 cubic meters of volume. Another bottle holds a volume of -8 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is -133 cubic meters.
Explanation: Add the volume of both bottles: -125 + (-8) = -133 cubic meters.
When the cube root of -125 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-5) = -10 The cube of -10 = -1000
When we multiply the cube root of -125 by 2, it results in a greater change in volume because the cube increases exponentially.
Find ∛(-64 + -61).
∛(-64 + -61) = ∛-125 = -5
As shown in the question ∛(-64 + -61), we can simplify that by adding them. So, -64 + -61 = -125. Then we use this step: ∛-125 = -5 to get the answer.
Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number. Perfect cube: A number that is the product of multiplying a number three times by itself. For example: (-5) × (-5) × (-5) = -125, therefore, -125 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In cube roots, ⅓ is the exponent which denotes the cube root of a number. Radical sign: The symbol that is used to represent a root, expressed as (∛). Negative number: A number that is less than zero, which can also have a real cube root as indicated in this example with -125.
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.
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