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 -27 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, ∛(-27) is written as (-27)^(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 -27, then y^3 can be -27. Since -27 is a perfect cube, the cube root of -27 is -3.
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 -27. The common methods we follow to find the cube root are given below: - Prime factorization method - Approximation method - Direct calculation for perfect cubes To find the cube root of a perfect number like -27, we can use direct calculation, recognizing that -27 is a perfect cube.
Let's find the cube root of -27 using direct calculation. Since -27 is a perfect cube, we know that (-3)^3 = -27. Therefore, the cube root of -27 is -3.
Finding the perfect cube of a number without any errors can be a challenging 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 box that has a total volume of -27 cubic units. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛(-27) = -3 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 -3 units.
A company manufactures -27 cubic meters of material. What would be the volume if they tripled the amount?
The new volume is -81 cubic meters.
To find the new volume, we multiply the original amount by 3: -27 * 3 = -81 cubic meters.
If the cube root of -27 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 * (-3) = -6 The cube of -6 = -216
When we multiply the cube root of -27 by 2, it results in a new value, -6. The cube of -6 is -216, which shows a significant increase in absolute volume.
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. For example, (-3) * (-3) * (-3) = -27, therefore, -27 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-27)^(1/3), ⅓ is the exponent which denotes the cube root. Radical sign: The symbol that is used to represent a root is expressed as (∛). Integer: A whole number that can be positive, negative, or zero. The cube root of -27 is an integer (-3).
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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