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 understanding the properties of materials and designing structures. We will now find the cube root of -3 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, ∛-3 is written as (-3)^(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 -3, then y^3 can be -3. Since the cube root of -3 is not an exact value, we can write it as approximately -1.4422.
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 -3. The common methods we follow to find the cube root are given below:
To find the cube root of a non-perfect number, we often follow Halley’s method.
Since -3 is not a perfect cube, we use Halley’s method.
Let's find the cube root of -3 using Halley’s method.
The formula is ∛a ≅ x((x^3 + 2a) / (2x^3 + a))
where:
a = the number for which the cube root is being calculated
x = the nearest perfect cube Substituting,
a = -3; x = -1
∛a ≅ -1(((-1)^3 + 2 × (-3)) / (2 × (-1)^3 + (-3)))
∛-3 ≅ -1((-1 - 6) / (-2 - 3)) ∛-3 ≅ -1.442
The cube root of -3 is approximately -1.4422.
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes that students commonly make and the ways to avoid them:
Imagine you have a cube-shaped object that has a total volume of -3 cubic units. Find the length of one side of the object equal to its cube root.
Side of the cube = ∛-3 ≈ -1.44 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 approximately -1.44 units.
A company has a material with a volume of -3 cubic meters. If the material is divided equally into 3 parts, what is the volume of each part?
The volume of each part is -1 cubic meters.
To find the volume of each part, we need to divide the total volume by 3: -3 / 3 = -1 cubic meters.
A container holds -3 cubic liters of liquid. If another container holds 5 cubic liters, what would be the total volume if the containers are combined?
The total volume of the combined containers is 2 cubic liters.
Explanation: Let’s add the volume of both containers: -3 + 5 = 2 cubic liters.
When the cube root of -3 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-1.44) = -2.88 The cube of -2.88 = -23.87
When we multiply the cube root of -3 by 2, it results in a significant change in the volume because the cube increases exponentially.
Find ∛(-3 + 5).
∛(-3 + 5) = ∛2 ≈ 1.26
As shown in the question ∛(-3 + 5), we can simplify that by adding them. So, -3 + 5 = 2. Then we use this step: ∛2 ≈ 1.26 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 is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-3)^(1/3), ⅓ is the exponent which denotes the cube root of -3. Radical sign: The symbol used to represent a root, expressed as (∛). Irrational number: Numbers that cannot be put in fractional forms are irrational. For example, the cube root of -3 is irrational because its decimal form goes on continuously without repeating the numbers.
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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