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 -9261 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, ∛(-9261) is written as (-9261)^(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 -9261, then y³ = -9261. The cube root of -9261 is an exact value, which is -21.
Finding the cube root of a number means identifying the number that must be multiplied three times to get the target number. Now, we will go through the different ways to find the cube root of -9261. The common methods we follow to find the cube root are given below:
To find the cube root of a perfect cube, like -9261, we can use the prime factorization method.
Let's find the cube root of -9261 using the prime factorization method:
1. Prime factorize -9261: -9261 = -1 × 21 × 21 × 21
2. The prime factors are grouped into triples: (-1 × 21) × (21²)
3. The cube root is the product of one factor from each group: ∛(-9261) = -21
The cube root of -9261 is -21.
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 students commonly make and the ways to avoid them:
Imagine you have a cube-shaped toy that has a total volume of -9261 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛(-9261) = -21 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 -21 units.
A company manufactures -9261 cubic meters of material. Calculate the amount of material left after using -3000 cubic meters.
The amount of material left is -6261 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount:
-9261 - (-3000)
= -6261 cubic meters.
A bottle holds -9261 cubic meters of volume. Another bottle holds a volume of -1000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is -10261 cubic meters.
Explanation: Let’s add the volume of both bottles: -9261 + (-1000) = -10261 cubic meters.
When the cube root of -9261 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-21) = -42
The cube of -42 = -74088
When we multiply the cube root of -9261 by 2, it results in a significant increase in the cube because the cube increases exponentially.
Find ∛(-92 + -169).
∛(-92 + -169) = ∛(-261) ≈ -6.41
As shown in the question ∛(-92 + -169), we can simplify that by adding them: -92 + -169 = -261.
Then we use this step: ∛(-261) ≈ -6.41 to get the answer.
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.
: He loves to play the quiz with kids through algebra to make kids love it.